A summer camp is organizing a hike and needs to buy granola bars for the campers. The granola bars come in small boxes and large boxes. Each small box has 6 granola bars and each large box has 24 granola bars. The camp bought 4 times as many small boxes as large boxes, which altogether had 96 granola bars. Graphically solve a system of equations in order to determine the number of small boxes purchased, x,x, and the number of large boxes purchased, yy.
Answers
Answer:
Let's define the variables:
x = number of small boxes bought.
y = number of large boxes bought.
Then the total number of granola bars is:
x*6 + y*24
We also know that "The camp bought 4 times as many small boxes as large boxes"
Then:
x = 4*y
and "...which altogether had 96 granola bars."
The total number of granola bars is 96, then:
x*6 + y*24 = 96
Then the system of equations is:
x = 4*y
x*6 + y*24 = 96
We want to solve this graphically.
Then we first need to isolate the same variable in both equations.
We can see that in the first one x is already isolated, so let's isolate x in the second equation:
x*6 = 96 - y*24
x = (96 - y*24)/6
x = 16 - y*4
Now we have the equations:
x = 4*y
x = 16 - y*4
To solve this graphically we need to graph both fo these lines and see in which point the lines do intersect.
The point where the lines intersect is the solution of the system.
The graph can be seen below.
We can see that the lines do intersect at the point (2, 8)
This means that the camp bought 2 large boxes and 8 small boxes.
Related Questions
An element with a mass of 700 grams decays by 6.1% per minute. To the nearest
tenth of a minute, how long will it be until there are 220 grams of the element
remaining?
Answers
Answer:
11.2 minutes
Step-by-step explanation:
If the element decreases by 6.1, every minute, it means that the mass lost every minute = 0.061 x 700g = 42.7g
The mass remaining after a minute = 657.30g
The equation that can be used to solve this question is :
700 - 42.7m = 220
m = minutes
Collect like terms
700 - 220 = 42.7m
480 = 42.7m
divide both sides of the equation by 42.7
m = 11.241218 minutes
the tenth is the first number after the decimal place. To convert to the nearest tenth, look at the number after the tenth (the hundredth). If the number is greater or equal to 5, add 1 to the tenth figure. If this is not the case, add zero
Here, the hundredth is less than 5, so zero would be added to 2. the answer is 11.2 minutes
Answer:
18.4
Step-by-step explanation:
I answered the question
what would be the distance between (-35,20) and (15,20).
Answers
Answer:
Well you just have to follow the formula to find the distance between 2 linear plots.
d= √(x2−x1)^2+(y2−y1)^2
Step-by-step explanation:
If you follow it the answer would be
D=50
please HELP! USE PYTHAGOREAN THEOREM TO FIND RIGHT TRIANGLE SIDE LENGTHS
formula A(2)+B(2)=C(2)
Answers
Answer:
x = √ 40
Step-by-step explanation:
6 x 6 = 36 2 x 2 = 4 36 + 4 = 40please help i have a test tomorrow
Answers
Answer:
a
b
e
Step-by-step explanation:
remember length times width equals area
1) 1/3(x+3)+1/6=1/2(x-1)-(x-3)
Answers
Answer:
x= 8/5
Step-by-step explanation:
Let's solve your equation step-by-step.
1
3
(x+3)+
1
6
=
1
2
(x−1)−(x−3)
Step 1: Simplify both sides of the equation.
1
3
(x+3)+
1
6
=
1
2
(x−1)−(x−3)
1
3
(x+3)+
1
6
=
1
2
(x−1)+−1(x−3)(Distribute the Negative Sign)
1
3
(x+3)+
1
6
=
1
2
(x−1)+−1x+(−1)(−3)
1
3
(x+3)+
1
6
=
1
2
(x−1)+−x+3
(
1
3
)(x)+(
1
3
)(3)+
1
6
=(
1
2
)(x)+(
1
2
)(−1)+−x+3(Distribute)
1
3
x+1+
1
6
=
1
2
x+
−1
2
+−x+3
(
1
3
x)+(1+
1
6
)=(
1
2
x+−x)+(
−1
2
+3)(Combine Like Terms)
1
3
x+
7
6
=
−1
2
x+
5
2
1
3
x+
7
6
=
−1
2
x+
5
2
Step 2: Add 1/2x to both sides.
1
3
x+
7
6
+
1
2
x=
−1
2
x+
5
2
+
1
2
x
5
6
x+
7
6
=
5
2
Step 3: Subtract 7/6 from both sides.
5
6
x+
7
6
−
7
6
=
5
2
−
7
6
5
6
x=
4
3
Step 4: Multiply both sides by 6/5.
(
6
5
)*(
5
6
x)=(
6
5
)*(
4
3
)
x=
8
5
Help plssssss I need it I’m failing life like uhhhhhh
Answers
Answer:
164
Step-by-step explanation:
15(5)
2(7)
15(5)
add em up
75 plus 14 plus 75
Which quadrilateral's diagonals are congruent and perpendicular bisectors of each other?
Answers
Diagonals congruent: rectangle, square, isosceles trapezoid
Perpendicular bisectors: Rhombus, Square
Please tell me how to round 14,780
Answers
Answer:
for 100: 14,800
for 10: 14,780
for 1: 14,780
for 1000: 15,000
Step-by-step explanation:
ok so just go for like if its
18 its going to be 20 if its 11 its going to be 10
Hope this helps!!
PLEASE CROWN TYY
Answer:
Rounding Rules:
1. If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up. Example: 38 rounded to the nearest ten is 40. ...
2. If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down. Example: 33 rounded to the nearest ten is 30.
Step-by-step explanation:
100: 14,800
10: 14,780
1: 14,780
1000: 15,000
Gary buys a 3 and 1/2 - pound bag of cat food every 3 weeks. Gary feeds his cat the same amount of food each
day. Which expression can Gary use to determine the number of pounds of cat food his cat eats each
year? (1 year = 52 weeks)
Answers
Answer:
546
Step-by-step explanation:
3 1/2 times 3 equals 10 1/2. 10 1/2 times 52 equals 546.
.222222222 as a fraction Please help
Answers
Answer:
222222222/1000000000
Step-by-step explanation:
Can someone please help me with this question
This is Amy's family.
Her family of 6 people(4 adults and 2 children) went to
Super Nintendo World last year. Although she couldn't
remember what each tickets costed, she knew that her
family paid $1700 total for the tickets,
use variable a for number of adult tickets
use variable c for number of child tickets
Write an equation that describes this situation,
Answers
Answer:
4a + 2c = 1700
Step-by-step explanation:
A store is having a buy one get one 30% off sale. During the sale Christopher buys two pairs of shoes that each have a regular price of 48$. How much does Christopher pay for the two pairs of shoes?
Answers
What type of triangle is this ?
Answers
Answer:
triangle bby
Step-by-step explanation:
Step-by-step explanation:
Right because there's an angle of 90
Hello, can someone please assist me with this problem.
Answers
The Pythagorean theorem is:
a^2 + b^2 = c^2
a = 1 and b = 3
1^2 + 3^2 = c^2
10 = c^2
square root of 10 = c
Now that we know the length of the side, we can find the area of the square. Area of a square = side^2, so:
Area = (square root of 10)^2 = 10
The area of the square is 10!
Un estudiante reparte el tiempo de un día de la siguiente forma:
1/4 del día duerme,
1/12 del día lo usa para desplazarse caminando hasta el colegio, 5/12
del día lo usa para estudiar. ¿Qué parte del día le queda para compartir con su familia?
Answers
Answer:
4 horas para compatir com su familia
Can I get help with this please I am so stuck in here
Answers
Answer:
the correct answer is d
hope it help
Based on a recent survey of 500 students,
the circle graph below shows how students
communicate
with friends.
How many more students chose social
media apps than phone calls to
communicate with friends?
A. 180 students
B. 12 students
C. 300 students
D. 36 students
Answers
Can someone please help me with this questions please help me I really need help please.
Answers
Answer:
C) Line A does not intersect Line B.
Step-by-step explanation:
Line A passes through (6 ,-30) & (-2 , 10)
Line B passes through (-4 , 28) & (2 , -2)
Find the slopes for each line. To find the slope, use the slope formula:
slope (m) = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
Line 1:
Let:
[tex](x_1 , y_1) = (6 , -30) \\(x_2 , y_2) = (-2 , 10)[/tex]
Plug in the corresponding numbers to the corresponding variables:
m = [tex]\frac{10 - (-30)}{-2 - 6} = \frac{10 + 30}{-8} = \frac{40}{-8} = \frac{-5}{1}[/tex]
Line 2:
Let:
[tex](x_1 , y_1) = (2 , -2)\\(x_2 , y_2) = (-4 , 28)[/tex]
Plug in the corresponding numbers to the corresponding variables:
m = [tex]\frac{28 - (-2)}{-4 - (2)} = \frac{28 + 2}{-4 - 2} = \frac{30}{-6} = \frac{-5}{1}[/tex]
The two lines share the same slope, therefore, they are parallel to each other. This means that they do not intersect at any given point.
Greg and cc went to the burger stand and bought dinner. Greg had 2 cheeseburgers and 5 fries. CC bought 3 cheeseburgers and 2 fries. Greg paid $24.75. CC also paid $24.75. How much would 2 cheeseburgers and 3 fries cost?
Answers
Answer:
20.00
Step-by-step explanation:
Aliyah spent half of her weekly allowance playing arcade games. To earn more money her parents let her mow the lawn for $7. What is her weekly allowance (W) if she ended up with $16? The variable should always go in the first term
Answers
Answer:
who mows the lawn for 7 dollars :/
Step-by-step explanation:
Jamie was surveying students about their use of the new science lab in a school. Which question in the survey is a statistical question?
Answers
Complete Question is:
Jamie was surveying students about their use of the new computer lab in a school. Which question in the survey is a STATISTICAL QUESTION?
A.) How qualified is the trainer at the computer lab?
B.) Where is the computer lab located in the school?
C.) What is the number of learning stations at the computer lab?
D.) How many class projects did you complete using the computer lab?
Answer:
D.) How many class projects did you complete using the computer lab?
The answer is D because the question is directly related to the use of their new computer lab and the number of projects the students have completed in the computer lab. This is directly related to the survey since it is carried out for the students using computer lab.
Yesterday, the temperature change for a 5-hour period of time was – -degree per
hour. Which statement describes this change?
A
The temperature rose 5 degrees.
B
The temperature rose 4 1/4 degrees.
с
The temperature fell 4 degrees.
D
The temperature fell 5 4/5
degrees
Answers
Answer:
D
Step-by-step explanation:
Over a 5-year period, a company reported annual profits of $8 million, $3 million, $2 million, and $9 million. In the fifth year, it reported a loss of $7 million. What was the mean annual profit?
Answers
Given
Annual profits of four years $8 million, $3 million, $2 million, and $9 million.
In the fifth year, it reported a loss of $7 million.
To find:
The mean annual profit.
Solution:
Formula for mean is:
[tex]\text{Mean}=\dfrac{\text{Sum of observations}}{\text{Number of observations}}[/tex]
Annual profits are $8 million, $3 million, $2 million, $9 million and -$7 million. Here negative sign represent loss.
So, the mean annual profit is:
[tex]\text{Mean}=\dfrac{8+3+2+9+(-7)}{5}[/tex]
[tex]\text{Mean}=\dfrac{22-7}{5}[/tex]
[tex]\text{Mean}=\dfrac{15}{5}[/tex]
[tex]\text{Mean}=3[/tex]
Therefore, the mean annual profit is $3 million.
Draw a two-dimensional representation of each prism. Then find the area of the entire surface of each prism
Answers
Answer:
Surface area of cuboid = 78 unit²
Step-by-step explanation:
Given diagram is a cuboid prism
Given:
Length of cuboid = 5 unit
Width of cuboid = 3 unit
Height of cuboid = 3 unit
Find:
Surface area of cuboid
Computation:
Surface area of cuboid = 2[lb + bh + hl]
Surface area of cuboid = 2[(5)(3) + (3)(3) + (3)(5)]
Surface area of cuboid = 2[15 + 9 + 15]
Surface area of cuboid = 2[39]
Surface area of cuboid = 78 unit²
What is the measure of the other acute angle.....?
I really need to get this right plsss help me ❤️ I really need to get to an 90
Answers
the answer is 30°
EXPLAINATION:
since the angle is a right angle triangle one of it's angles is 90°, and all the angles of a triangle always add up to 180°
so, 90° + 60° + x = 180
150° + x = 180°
so x = 180° - 150° = 30°
hence, the other acute angle is 30°.
Which expression is equivalent to (-3)x+(3)(-12)?
Answers
Answer:
Step-by-step explanation:
(-3)x + (3)(-12)
= -3x -36
or -3(x + 12)
Answer:
Step-by-step explanation:
(-3)x + 3(-12) = (-3) (x + 12)
(-3) is both the two terms. So we can take (-3) as common
yo i need help please i need the correct answer i will give u a brainliest to please just help me
Answers
Answer:
a
Step-by-step explanation:
Lindsay and Lorraine are trying to match the jump rope world record. Together, they need to jump 48 times in a row. Lindsay has gotten 14 jumps in a row, and Lorraine has gotten 13. Write an equation using (j) as the variable and show your work to determine how many more jumps they need to complete.
( if u steal my points ill steal yours)
(no links or ill report)
Answers
Answer: They need to complete 21 more jumps all together .
Step-by-step explanation: So 14+13=J
14+13=27
27=j
World record: 48; 48-27=21
They will have to jump 21 more times in a row .
Which expression is equivalent to 5(2+7)?
Answers
Answer:
I can help you but first I need the rest of the answers to find out what's it equivalent to.
Use completing the square to find the equation of the following circle in standard form.
x2 + y2 - 4x + 12y - 16 = 0
Answers
Answer:
Here's a calculator that should help
Step-by-step explanation:
https://www.calculatorsoup.com/calculators/algebra/completing-the-square-calculator.php