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KiRa [710]
3 years ago
5

Trisha and Byron are washing and vacuuming cars to raise money for a class trip. Trisha raised $38 washington 5 cars and vacuumi

ng 4 cars. Byron raises $28 by washing 4 cars and vacuuming 2 cars. Find the amount they charged to wash a car and vacuum a car.
Mathematics
1 answer:
ANEK [815]3 years ago
8 0

Answer:

They charged <u>$6</u> for washing and <u>$2</u> for vacuuming the car.

Step-by-step explanation:

Let the charge of washing a car be 'x'.

And also let the charge of vacuuming a car be 'y'.

Now according to question, Trisha raised $38 washing 5 cars and vacuuming 4 cars.

So framing the above sentence in equation form, we get;

5x+4y=38\ \ \ \ \ equation\ 1

Again according to question, Byron raises $28 by washing 4 cars and vacuuming 2 cars.

So framing the above sentence in equation form, we get;

4x+2y=28\ \ \ \ \ equation\2

Now multiplying equation 2 by '2', we get;

2(4x+2y)=28\times2\\\\8x+4y=56\ \ \ \ equation\ 3

Now we subtract equation 1 from equation 3 and get;

(8x+4y)-(5x+4y)=56-38\\\\8x+4y-5x-4y=18\\\\3x=18\\\\x=\frac{18}{3}=6

Now substituting the value of 'x' in equation 1, we get;

5x+4y=38\\\\5\times6+4y=38\\\\30+4y=38\\\\4y=38-30=8\\\\y=\frac{8}{4}=2

Hence They charged <u>$6</u> for washing and <u>$2</u> for vacuuming the car.

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In triangle △ABC, ∠ABC=90°, BH is an altitude. Find the missing lengths. AC=5 and BH=2, find AH and CH.
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Step-by-step explanation:

An altitude divides a right triangle into similar triangles. That means the sides are in proportion, so ...

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The problem statement tells us AH + CH = AC = 5, so we can write

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This gives us the quadratic ...

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