1. “Systems of Linear Equations”
American Airlines sold a certain number of tickets from Los Angeles to Hawaii. They charged $90
for flight x and the remaining tickets for $250 for flight y. If the airline sold 120 tickets and
collected a total of $27,600 from the sale of those tickets:
a) Set up the System of Linear Equations
b) How many tickets of each flight were sold?
c) How much money was made from each flight?
Answers
Answer:
Part A)
[tex]\begin{aligned} x+y&=120 \\ 90x+250y&=27600\end{aligned}[/tex]
Part B)
Flight X sold 15 tickets and Flight Y sold 105 tickets.
Part C)
Flight X made $1,350 and Flight Y made $26,250.
Step-by-step explanation:
Let the amount of tickets sold by Flight X be represented by x and the amount of tickets sold by Flight Y be represented by y.
Part A)
The airline sold 120 tickets in total. Hence:
[tex]x+y=120[/tex]
Each x ticket costs $90 and each y ticket costs 250. The total income was $27,600. Thus:
[tex]90x+250y=27600[/tex]
Our system of equations is:
[tex]\begin{aligned} x+y&=120 \\ 90x+250y&=27600\end{aligned}[/tex]
Part B)
Solve the system of equations. We can use substitution. From the first equation, subtract y from both sides:
[tex]x=120-y[/tex]
In the second equation, we can divide everything by 10 and substitute in x:
[tex]9(120-y)+25y=2760[/tex]
Simplify:
[tex]16y+1080=2760[/tex]
So:
[tex]y=105\text{ tickets}[/tex]
Using the equation above:
[tex]x=120-(105)=15\text{ tickets}[/tex]
Flight X sold 15 tickets and Flight Y sold 105 tickets.
Part C)
Since each ticket of Flight X sold for $90 and Flight X sold 15 tickets, Flight X made $1,350.
Then it follows that Flight Y made $26,250.
Related Questions
Coffee is sold in two different-sized canisters. The smaller canister has a diameter of 9 cm and a height of 12 cm. The larger canister is double the size of the small canister. Calculate the volume and surface area of each canister and compare the results of doubling the dimensions.
Answers
Answer:
Step-by-step explanation:
Smaller Canister:
Height, h = 12cm
Diameter = 9cm
Radius, r = 4.5 cm
[tex]Volume = \pi r^2h\\[/tex]
[tex]=\pi \times 4.5^2 \times 12\\\\=243 \pi \ cm^3[/tex]
[tex]Surface \ area = 2 \pi r(r + h)\\[/tex]
[tex]=2 \times \pi \times 4.5 ( 4.5 + 12)\\\\= \pi \times 9(16.5)\\\\=148.5 \ cm^2[/tex]
Larger Canister:
Measures double the smaller canister, that is
height, H = 24 cm
Diameter = 18cm
Radius, R = 9cm
[tex]Volume = \pi R^2 H\\[/tex]
[tex]= \pi \times 9^2 \times 24\\\\= \pi \times 81 \times 24 \\\\= 1944 \pi[/tex]
[tex]Surface \ area = 2 \pi R(R+ H)[/tex]
[tex]= \pi \times 2 \times 9 ( 9 + 24) \\\\= \pi \times 18(33)\\\\=594 \pi \ cm^2[/tex]
Comparing results :
[tex]Volume_{small} = \pi r^2 h\\\\Volume_{large} = \pi R^2 H = \pi(2r)^2(2h) = \pi(4r^2)(2h)= 8 \pi r^2h = 8 \times volume_{small}[/tex]
Therefore, volume of larger canister is 8 times the volume of smaller canister.
[tex]Surface\ area _{larger} = 2 \pi R(R + H) = 2 \pi(2r)((2r+2h))\\\\[/tex]
[tex]=2 \ pi \times 2r \times 2 (r+ h)\\\\= 4 \times 2\pi r(r+ h) \\\\= 4 \times surface\ area_{smaller}[/tex]
Therefore, surface area of larger canister is 4 times the surface area of smaller canister.
f(x) = 3x² + 7x; g(x) = 6x +3; f(x) - g(x) =
Answers
Answer:
[tex] = 3x {}^{2} + x - 3[/tex]
Can someone help me with this? Will Mark brainliest.
Answers
The answer should be diameter.
Answer:
diameter
Step-by-step explanation:
Who answered the most questions correctly
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Find (from (3)
f(x) = x^2 - x
Answers
Answer:
I think the answer is 6.......
Emma says the length of her favorite movie is 120120120 minutes, but she has rounded the time to the nearest ten.
Which could be the number of minutes of Emma's favorite movie before she rounded it?
Answers
Answer:
17
Step-by-step explanation:
Which angels are corresponding angles
Answers
Answer:
B. 5 and 7
E. 1 and 3
F. 6 and 8
Step-by-step explanation:
The angles in matching corners are called corresponding angles.
Could really use some help! i meed it bad
Answers
Answer:
b= 10
Step-by-step explanation:
h=2b, (bh/2)=100, bh=100, b^2=100, b=10
Evaluate the expression when x = 4.
6(x + 8)
Answers
Answer:
6x+48
Step-by-step explanation:
6(x+8)
=(6)(x+8)
=(6)(x)+(6)(8)
=6x+48
Answer:
72
Step-by-step explanation:
6(4+8)
6(12)
the answer is 72
If 5x – 3y = 1 and
x - 2y = - 4, then xy = ? .
A 5
B 4
© 6
D 8
E 9
Answers
Answer:
[tex]6[/tex]
The answer is C:6
5x -3y=1......eq 1
x-2y=-4 ......eq2
From equation 2 too we can write
x = -4 + 2y ... put this x value on eq 1 so
5(-4+2y) - 3y = 1
-20 + 10y -3y=1
Or, 7y=21
So y=21/7=3
And put the value of y on equation 2
x -2 X 3 =-4
Or x= -4+6
So x=2 answer from question too we get value of x and y is 2,3 so
xy= 2X3=6 answer
PLS HELP! 20 POINTS!
Answers
Explanation: Because first we did the reciprocal then we simplified the expressions.
help me please really need it
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Answer:
it's just a sussy baka and it cannot be that bad im feeling like imposter i might just be a monster
Step-by-step explanation:
Amongus in real life
sus caught in 4k camera
Which long division problem can be used to prove the formula for factoring the difference of two perfect cubes?
Answers
It’s 69
“Explaining “
Answer:
The answer would be D
Step-by-step explanation:
Got it right on Edge 2021
Tracey paid $374.25 for a new iPad. What was the original cost if the iPad was on sale for 25% off
Answers
Answer:
$467.8125
Step-by-step explanation:
Percentage increase = 25% × 374.25
New value = 374.25 + Percentage increase
New value =
374.25 + Percentage increase =
374.25 + (25% × 374.25) =
374.25 + 25% × 374.25 =
(1 + 25%) × 374.25 =
(100% + 25%) × 374.25 =
125% × 374.25 =
125 ÷ 100 × 374.25 =
125 × 374.25 ÷ 100 =
46,781.25 ÷ 100 =
467.8125 ≈
467.81
Someone help me please!
Answers
Answer:
y < -3x + 2
Step-by-step explanation:
The shading is below the line meaning the inequality is less than. Moreover, the line is dashed meaning there is no 'equal to'.
Therefore, the inequality is y < -3x + 2.
Which expression is equivalent to
Answers
Answer:
[tex] x {4}[/tex]
Step-by-step explanation:
easy math
The wheely fast co. Makes custom skateboards for professional riders. They model their profit with the relation P=-2b^2 + 14b - 20, where b is the number of skateboards they produce(in thousands) and P is the company's profit in hundred thousands of dollars. When does wheely fast break even?
Answers
Answer:
The answer is below
Step-by-step explanation:
Breakeven point is the point of balance where their is neither a loss or a profit. At the breakeven point, the revenue gotten from the sell of goods is equal to the cost of production of the goods, hence the profit is zero.
Given the profit function:
P=-2b² + 14b - 20
At breakeven P = 0, hence:
0 = -2b² + 14b - 20
-2b² + 14b - 20 = 0
-2b² + 10b + 4b - 20 = 0
-2b (b - 5) + 4(b - 5) = 0
(b - 5)(-2b + 4) = 0
b - 5 = 0; or -2b + 4 = 0
b = 5; or b = 2
Since b is in thousands, hence the company breaks even when the number of skateboards produced is either 2000 or 5000
Having ____ siblings is just as common as having____
Answers
They both have the same amount of X’s
Answer:
1 ; 3
Step-by-step explanation:
Hope this answer helps you :)
Have a great day
Mark brainliest
Benjamin needs $0.75 more cents to buy a granola bar that costs $1.89. How much money does Benjamin have now? The equation that correctly models the problem is To undo what has been done to the variable on both sides of the equation. The solution of the equation is
Answers
✔ b + 0.75 = 1.89
✔ subtract 0.75
✔ b = $1.14
the person above me doesn't make since so here the answers
Benjamin presently have $1.14.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
Benjamin needs $0.75 more cents to buy a granola bar that costs $1.89.
let Benjamin have the amount $b.
So, the Expression to represent the situation is:
b + 0.75 = 1.89
Now, subtract 0.75 from both side
b + 0.75 - 0.75 = 1.89 - 0.75
b = 1.14
Learn more about Equation here:
https://brainly.com/question/29657983
#SPJ6
find the missing number in the factor tree
for 20 points
i hope you will help
Answers
Answer:
see below
Step-by-step explanation:
80 = 4* 20
2*2 2 * 10
2 *5
We are breaking the numbers into primes
2*2*2*2*5
HELP ASPA WILL GIVE BRAINLISET
A pizza delivery man makes $50.00 a shift. If he makes $3.00 on each delivery he makes, how much will he make if he makes 22 deliveries in one shift? Create an equation to represent this situation. Write the equation in function notation. State the ordered pair for 22 deliveries and explain your solution.
Answers
Answer:
f(x) = 3x + 50 is the equation in function notation.
(22, 116) is the ordered pair for 22 deliveries.
Step-by-step explanation:
First, create the equation. Let x represent how many deliveries he makes.
Since he makes $3 on each delivery, the total amount he makes from deliveries can be represented by 3x.
He also makes $50 a shift, so add this to 3x in the equation:
f(x) = 3x + 50 is the equation in function notation.
Find how much he will make if makes 22 deliveries. Plug in 22 as x:
f(x) = 3x + 50
f(22) = 3(22) + 50
f(22) = 66 + 50
f(22) = 116
So, he will make $116.
As an ordered pair, the solution is (22, 116).
Answer:
f(x) = 3x + 50
Step-by-step explanation:
If he makes $50.00 a shift, and $3.00 for each delivery, and he makes 22 deliveries in one shift then the equation (in function notation) would be f(x) = 3x + 50. and the solution to the equation is 116.
What is the slope-intercept form equation of the line that passes through (2, 4) and (4, 10)?
O y = -3x - 2
O y = -3x + 2
O y = 3x + 2
O y = 3x - 2
Answers
⊹˚ʚ ❑Answer︰The slope is 3!
⊹˚ʚ ❑Explanation︰use the formula y2-y1 over x2-x1
✎Daily reminder: make sure to eat food and stay hydrated, have a good day :D
Answer:
y = 3x - 2.
Step-by-step explanation:
The slope of the line (m) = (10-4)/(4-2)
= 3.
y - y1 = m(x - x1)
y - 10 = 3(x - 4)
y = 3x - 12 + 10
y = 3x - 2.
Someone help me please
Answers
Answer:
h. I dont understand the question-
i. 2w + 5
j. 7m + 13s (I didnt get the second number)
k. -2x + 3y (I also didnt get the first number-)
l. 5c - 2d
m. 10a + 2g
n. 5a + 12
Step-by-step explanation:
please help asap!!!! will mark brainliest
Answers
Answer:
A 9x--12 i hope this helps
Answer:
a. 9x-12
Step-by-step explanation:
Perimeter means total length of sides.
So, add (2x-7)+(5x-3)+(2x-2)
9x-12
HELPP WILL GIVE BRAINLEST !!!!!!!!
Answers
Answer:
8.06
Step-by-step explanation:
please help me with homework or i will get yelled by my teachers lolz
Answers
Answer:
the answer to this is 7.
Step-by-step explanation:
7+3=10.
uhmm bcos 3 + 7 = 10
Easy eh?-
Triangle ABC is similar to triangle EFD. What scale factor is required to dilate triangle ABC so that it's image, A'B'C' , is congruent to triangle EFD
Answers
The members of a golf team contributed a total of $14.30 for a party to be held after their practice. Each member contributed the same amount of money in dimes only. How many members are in the team and how much money did everyone contribute? Give all possible answers.
Answers
Answer:
each teammate contributed 1.43 sorry but i do not know how many members they have because my head hurts
System of equations, please help.
Answers
Answer:
3.75*A + 2.50*D = 35
A + D = 12
A = 12 - D
3.75*(12-D) +2.5*D= 35
45 - 3.75D + 2.5D = 35
45 - 1.25D = 35 |-35
10 - 1.25D = 0 |+1.25D
10 = 1.25D | /1.25
8 = D
A+D=12
A+8=12 |-8
A=4
If you like it, brainliest would be cool
Please help! (slopes and grafts) (multiple choice)
Answers
Answer:
slope = 2
Step-by-step explanation: