Elvira, the cafeteria manager, has just received a shipment of new trays with the school logo prominently displayed in the middle of the tray. After unloading 4 cartons of trays in the pizza line, she realizes that students are arriving for lunch and she will have to wait until lunch is over before unloading the remaining cartons. The new trays are very popular and in just a couple of minutes 24 students have passed through the pizza line and are showing off the school logo on the trays. At this time, Elvira decides to divide the remaining trays in the pizza line into 3 equal groups so she can also place some in the salad line and the sandwich line, hoping to attract students to the other lines. After doing so, she realizes that each of the three serving lines has only 12 of the new trays. "That's not many trays for each line. I wonder how many trays there were in each of the cartons I unloaded?"


Help the cafeteria manager answer her question using the data in the story about each of the actions she took. Explain how you arrive at your solution.

Answers

Answer 1

Answer:

im willing to bet that there is 3 in each carton

(just a guess for the points also theres no multiple choice?)

Answer 2

The quantity of trays that were in each of the cartons the manager unloaded was 12 trays.

How many trays there were in each of the cartons I unloaded?

To determine the quantity of trays in each carton, we need to analyze the given information step by step:

We know that 24 students have passed through the pizza line and received trays with the school logo.The remaining trays were divided into three equal groups for the salad line, sandwich line, and pizza line.Each serving line ended up with only 12 new trays.

From these points, we can deduce the following:

Since 24 students passed through the pizza line, and each student received one tray, this means that 24 trays were taken from the initial shipment.After 24 trays were taken, an equal number of trays were distributed to the salad line, sandwich line, and the remaining trays were kept in the pizza line.Each serving line ended up with 12 new trays. Since the trays were divided equally among the three lines, each line received the same number of trays.

Now, let's solve for the number of trays in each carton.

Let's assume that the number of trays in each carton is "x."

We know that 24 trays were taken initially, and each serving line ended up with 12 trays. So, we can set up the equation:

24 + 12 + 12 + 12 = 4x

48 = 4x

Dividing both sides of the equation by 4:

12 = x

Therefore, there were 12 trays in each of the cartons that were unloaded.

To summarize, each carton that Elvira unloaded contained 12 trays.

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Related Questions

Use long division to find the quotient below.
(8x3 + 4x2 + 100) = (2x + 5)
A. 4x2 + 12x + 20
B. 4x2 + 8x+ 20
C. 4x2 - 12x+ 20
D. 4x2 - 8x + 20

Answers

Answer:

D

Step-by-step explanation:

D 4x2-8x+20

In Triangle BCD, BC=BD, and angle B =13x-35, angle C = 5x-19, angle D=2x+14. Find the measure of each angle

Answers

Answer:

[tex]B = 108[/tex]

[tex]C = 36[/tex]

[tex]D = 36[/tex]

Step-by-step explanation:

Given

[tex]B =13x - 35[/tex]

[tex]C = 5x - 19[/tex]

[tex]D=2x+14[/tex]

[tex]BC = BD[/tex]

Required

Determine the measure of each angle

The angles in a triangle sum up t 180. i.e.

[tex]B + C + D = 180[/tex]

Since [tex]BC = BD[/tex], then [tex]C = D[/tex]

[tex]B + C + D = 180[/tex] can then be rewritten as:

[tex]B + C + C = 180[/tex]

[tex]B + 2C = 180[/tex]

Substitute values for B and C

[tex]13x - 35 + 2(5x - 19) = 180[/tex]

Open Bracket

[tex]13x - 35 + 10x - 38 = 180[/tex]

Collect Like Terms

[tex]13x + 10x = 180 + 38 + 35[/tex]

[tex]23x= 253[/tex]

Divide both sides by 23

[tex]x = 11[/tex]

To get the measure of each angle, substitute 11 for x in the expressions of B, C and D

[tex]B =13x - 35[/tex]

[tex]B = 13 * 11 - 35[/tex]

[tex]B = 108[/tex]

[tex]C = 5x - 19[/tex]

[tex]C = 5 * 11 - 19[/tex]

[tex]C = 36[/tex]

[tex]D=2x+14[/tex]

[tex]D = 2 * 11 + 14[/tex]

[tex]D = 36[/tex]

The measure of m<B, m<C and m<D are 108, 36 and 46 respectively

What are triangles?

From the triangle BCD, if BC=BD, then

m<C = m<D (Base angles are equal)

Given the following paramters:

m<C = 5x-19m<D = 2x + 14

Hence;

5x - 19 =2x + 14

5x- 2x = 14 + 19

3x = 33

x = 11

m<B = 13x - 35

m<B = 13(11) - 35

m<B = 108 degres

m<C = 5x - 19

m<C = 55- 19

m<C = 36

m<D = 180 - 144

m<D = 36 degreees

Hence the measure of m<B, m<C and m<D are 108, 36 and 46 respectively

learn more on angles here: https://brainly.com/question/16281260

x squared = 4x squared -75

Answers

X^2 = 4x^2 - 75
-3x^2 = -75
X^2 = 25
X = -5, 5

Please help me out!!!! I’m struggling

Answers

Answer:

SSS

Step-by-step explanation:

Add 3 level scoops of mini chocolate chips and 1 level scoop of raisins to Container 1. If each scoop has the same number of items, what percent of the items in Container 1 are mini chocolate chips? (This value is known as the percent concentration of chips.) Explain how you decided. Label the container appropriately Answer: 50% because when there is only 2 variables and they are each 1 cup there is an even amount of stuff and when you ask for only one percentage that would be 50% because everything is even. Even if you asked for the percentage for the cup of raisins it would also be 50% Add 2 scoops of mini chocolate chips and 3 scoops of raisins to Container 2. What is the percent concentration of mini chocolate chips? Explain how you decided. Label the container appropriately. Stir the chips and raisins in each container to ensure that the chips and raisins are evenly mixed.

Answers

Answer:

Container 1  

The percentage of mini chocolate chip is 3/4 * 100= 75 % to raisins.

Container 2

The percentage of mini chocolate chip is 2/5 * 100= 40 % to raisins.

Step-by-step explanation:

Container 1  

Mini Chocolate Chips:  Raisins

3 scoops: 1 scoop

The percentage of mini chocolate chip is 3/4 * 100= 75 % to raisins.

Container 2

Mini Chocolate Chips:  Raisins

2 scoops: 3 scoop

The percentage of mini chocolate chip is 2/5 * 100= 40 % to raisins.

This is simplified with the help of the ratios . We find out the ratio of the mini chocolate to the total of both the ratios and mulitply it with 100 to get the percentage concentration.

estimate 1scoop chips and 2scoops rice percentage

The lengths of four insects are 0.02 inch, 1 8 inch, 0.1 inch, and 2 3 inch. List the lengths in inches from least to greatest.

Answers

Answer:

0.1,0.2,1.8,2.3

Step-by-step explanation:

Answer:

.02, .1, 1/8, 2/3

Step-by-step explanation:

BRAINLEIST AND 5 STARS The function gives the number of people, in millions, who own a smartphone, years after the year 2000.
What does each equation tell us about smartphone ownership?
P(17) = 2, 320

Answers

Anwser:


It tells us that we would multiply Px 17 and that it is equal to the amount of years they get

Ps. Hope this helps

plz help me its do today

Answers

y int: 5
equation: -2/3x +5
slope: -2/3

How many times would Thor jump in 2 hours if he jumped 3 times every 5 minutes?

Answers

Answer:

72

Step-by-step explanation:

Answer:

72

Step-by-step explanation:

There are 12 five minutes in an hour, so 24 five minutes in two hours.

3*24=72.

What is the slope of the line?

Answers

Get two coordinates from the graph
(0,1) and (1,3)
Use them to find gradient
(3-1)/(1-0)=2

Write this ratio as a fraction in simplest form
140 centimeters to 300 centimeters
Answer choices:
A. 14/30
B. 4/7
C. 1/3
D. 7/15

Answers

Answer:

D

140/300 simplifies to 14/30 and that can be simplified even more to 7/15

A gas station sells unleaded regular and unleaded premium gasoline. The price per gallon charged by the station is$1.299 for unleaded regular and $1.379 for unleaded premium. The cost per gallon from supplier is$1.219 for unleaded regular and $1.289 for unleaded premium. If equals the number of gallons sold of regular and equals the number of gallons sold of premium:(a) Formulate the revenue function from selling and gallons of the two grades of gasoline respectively?(b) Formulate total cost for purchasing and gallons?(c) Formulate the total profit? d) what is the total profit expected to equal if the station sells 100,000 gallons of unleaded and regular and 40000 of unleaded premuim?

Answers

Answer:

a) Revenue function = 1.299r + 1.379p

where: r = gallon of unleaded regular gasoline and p = gallon of regular unleaded premium gasoline

b) cost function = 1.219f + 1.289p

c) profit function = (1.299r + 1.379p) - (1.219f + 1.289p) = 1.299r - 1.219r + 1.379p - 1.289p = 0.08p + 0.09p

d) total profit = (0.08 x 100,000) + (0.09 x 40,000) = $8,000 + $3,600 = $11,600

4.5(8 - x) + 36 = 102 - 2.5(3x + 24)

Answers

Answer:

x = -10

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDASEquality Properties

Step-by-step explanation:

Step 1: Define equation

4.5(8 - x) + 36 = 102 - 2.5(3x + 24)

Step 2: Solve for x

Distribute:                                   36 - 4.5x + 36 = 102 - 7.5x - 60Combine like terms:                   -4.5x + 72 = -7.5x + 42Add 7.5x on both sides:             3x + 72 = 42Subtract 72 on both sides:        3x = -30Divide 3 on both sides:              x = -10

Step 3: Check

Plug in x into the original equation to verify it's a solution.

Substitute in x:                    4.5(8 - -10) + 36 = 102 - 2.5(3(-10) + 24)Simplify:                               4.5(8 + 10) + 36 = 102 - 2.5(3(-10) + 24)Multiply:                               4.5(8 + 10) + 36 = 102 - 2.5(-30 + 24)Add:                                     4.5(18) + 36 = 102 - 2.5(-6)Multiply:                               81 + 36 = 102 + 15Add:                                     117 = 117

Here we see that 117 does indeed equal to 117.

∴ x = -10 is a solution of the equation.

Isaiah is working two summer jobs, making $16 per hour tutoring and $10 per hour clearing tables. isaiah must earn at least $110 this week. write an inequality that would represent the possible values for the number of hours tutoring, t, and the number of hours clearing tables, c, that isiah can work in a given week​

Answers

Answer:

16t + 10x = 110

Step-by-step explanation:

t = tutoring

x = cleaning tables

16t + 10x = 110

All you do is plug in numbers.

Answer:

16t + 10c>=110

Step-by-step explanation:

the total earned from tutoring in a week is

16(t)

and the total earning from clearing tables per week is

10(c)

but in a week he has to earn a minimum of 110 dollars

Pls help asappp solve for x

Answers

X= I ain’t never seen two pretty best friends, one of them always gotta be ugly

Answer:

65

Step-by-step explanation:

If you need explanation please tell me.

$25 with a 300% increase

Answers

Answer:

100 dollars

Step-by-step explanation:

So amount of increase = (300/100) * 25

                                      = 3 * 25

                                      = 75 dollars

Then the final amount = (25 + 75) dollars

                                  = 100 dollars

Molly is making bags of trail mix for the hiking club. She will use 20 ounces of walnuts. 11.1 ounces of almonds, and 24.8 ounces of cashews. This amount makes 26 bags of trail mix. How many ounces are in each bag?

Answers

Answer:

2.15 ounces

Step-by-step explanation:

The total ounces of nuts in the bag is calculated as:

20 ounces of walnuts + 11.1 ounces of almonds + 24.8 ounces of cashews = 55.9 ounces.

From the question we are told that these amounts make 26 bags.

The number of ounces that are in each bag is calculated as:

26 bags = 55.9 ounces

1 bag = x ounces

Cross Multiply

26 bags × x ounces = 1 bag × 55.9 ounces

x ounces = 1 bag × 55.9 ounces/26 bags

x ounces = 2.15 ounces

Therefore, there are 1.94 ounces in each bag

A recipe calls for 3 cups of flour to 4 cups of sugar. Find the unit rate of flour to cups of sugar.

Answers

Answer: 0.75 cups of flour to 1 cup of sugar.

Step-by-step explanation:

From the question, we are informed that a recipe calls for 3 cups of flour to 4 cups of sugar and told to calculate the unit rate.

It simply means what we need to calculate much of flour to one cup of sugar. This will be:

= 3/4 = 0.75

Therefore, the unit rate will be:

0.75 cups of flour to 1 cup of sugar.

PLEASE HELP ME

An alloy is a mixture of metals.Suppose that a certain alloy is made by mixing 70 grams of an alloy that contains 12% copper with 90 grams of pure copper.

Answer the questions below. Do not do any rounding.

(a) How many grams of copper are in the resulting mixture?

Il grams

(b) What percentage of the resulting mixture is copper?

Answers

Answer:

(a) How many grams of copper are in the resulting mixture?

= 160 grams

(b) What percentage of the resulting mixture is copper?

= 61.5%

Step-by-step explanation:

(a) How many grams of copper are in the resulting mixture?

From the question: Suppose that a certain alloy is made by mixing 70 grams of an alloy that contains 12% copper with 90 grams of pure copper.

The number of grams of copper in the resulting mixture = 70 grams + 90 grams = 160 grams

(b) What percentage of the resulting mixture is copper?

70 grams of an alloy that contains 12% copper = 70 × 12%

= 70 grams × 0.12

= 8.4 grams

The number of grams of copper in the resulting mixture = 160 grams

The percentage of the resulting mixture that is copper is

=( 8.4 grams + 90 grams of pure copper/160) × 100

= 98.4/160 × 100

= 61.5%

In row 2, write the equation of a quadratic function that satisfies f(0) = 2.

Answers

assuming this means y=2 and x=0

you can use the equation y=x+2

y=3/8x−4 write in standard form

Answers

Answer:

y=3/8x-4
Move the expression to the left
y-3/8x=-4
Multiply both sides by 8
8y-3x=-32
Reorder the terms
-3x+8y=-32
Change the signs and standard form is...
3x-8y=32


Answer:

3x-8y=32

Step-by-step explanation:

-30<x/-4 answer must be simplified ​

Answers

Answer:

x<120

Step-by-step explanation:

-30<x/-4

In order to simplify this, we must isolate the x value by multiplying both sides by -4

Since we are dealing with inequalities and we are multiplying by a negative number, we have to switch the sign (<,>)

-30(-4)>x

x<120

3. + (-2) + (-24 )
Please help this question is worth a lot of points ( math question) help please:)

Answers

Answer:

[tex] \huge{ \boxed{ \bold{ \sf{ - 26}}}}[/tex]

☄ Question : Simplify[tex] \sf{ + ( - 2) + ( - 24)}[/tex]☄ Step - by - step explanation : [tex] \sf{ + ( - 2) + ( - 24)}[/tex]

Remember : [tex] \sf{( + ) \times ( - ) = ( - )} [/tex]

[tex] \dashrightarrow{ \sf{ - 2 - 24}}[/tex]

Remember : The negative integers are always added but posses the negative ( - ) sign.

[tex] \dashrightarrow{ \boxed{ \sf{ - 26}}}[/tex]

--------------------------------------------------------------

† Remember :

Sign rules of addition and subtraction of integers :

The positive integers are always added but posses the positive ( + ) sign.The negative integers are always added but posses the negative ( - ) sign.The negative and positive integers are always subtracted but posses the sign of the bigger integer.

Sign rules of multiplication and division :

[tex] \sf{( + ) \times ( + ) = ( + )}[/tex][tex] \sf{( + ) \times ( - ) = ( - )}[/tex][tex] \sf{( - ) \times ( + ) = ( - ) }[/tex][tex] \sf{( - ) \times ( - ) = ( + ) }[/tex]

▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁

Hope I helped!

Have a wonderful time ! ツ

80 students were at the volleyball game.
Some went home and now there are only 52. What is the percent of change?

Answers

35% people went home

f(x) = x2. What is g(x)?

Answers

Answer:

its C. yw

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

i did the test

what is 1/2 of 6/7 ​

Answers

Answer:

3/7

Step-by-step explanation:

6/14 which equals 3/7

f(x) = -4x – 2, solve for x when f(x) = 6

Answers

Step-by-step explanation:

[tex] - 4x - 2 = 6[/tex]

[tex] - 4x = 8[/tex]

[tex]x = - 2[/tex]

Which of the following is an example of a Unit Rate?

A 10 pounds of apples cost $4.

B Each marker costs $0.50.

C Steve runs 3 miles in 20 minutes.

D A half sub costs $2.50.

Answers

Answer:

B each marker cost $.50

Step-by-step explanation:

Question: If an electric train is moving north at 100mph and a wind is blowing to the west at 10mph, which way does the smoke blow?

Answers

Answer:

There is no smoke due to it being an electric train.

Step-by-step explanation:

Didn't fool me. ;)

that question has already been answered: https://brainly.com/question/4480585

Jason bought a new truck at $25,000. The truck depreciates 15% of its value continuously each year. How much is it worth after 5 years? Round the answer to nearest dollar.

Answers

Answer:

A = $11093

Step-by-step explanation:

Given the following data;

Principal = $25,000

Rate = 15% = 15/100 = 0.15

Time, t = 5

To find the future value, we would use the compound interest formula;

[tex] A = P(1 + \frac{r}{n})^{nt}[/tex]

Where;

A is the future value. P is the principal or starting amount. r is annual interest rate. n is the number of times the interest is compounded in a year. t is the number of years for the compound interest.

Substituting into the equation, we have;

r = -0.15 because it's depreciating.

[tex] A = 25000(1 + \frac{-0.15}{1})^{1*5}[/tex]

[tex] A = 25000(1 - 0.15)^{5}[/tex]

[tex] A = 25000(0.85)^{5}[/tex]

[tex] A = 25000*0.4437[/tex]

A = 11092.63 ≈ $11093

Therefore, the future value, A after 5 years is $11093.

Answer:

11809

Step-by-step explanation:

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