The drama club is having a car wash as a fundraiser. They wash cars for $5 each and trucks for $8 each. How many of each type of vehicle did they wash if they raised $199 by washing 32 vehicles?

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The drama club is having a car wash as a fundraiser. They wash cars for $5 each and trucks for $8 each. How many of each type of vehicle did they wash if they raised $199 by washing 32 vehicles?

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Answer 1 · 2017-11-20T04:52:29

19 cars, 13 trucks

Explanation:

Okay, let's start by defining our variables

$c =$ $c=$ number of cars

$t =$ $t=$ number of trucks

There are 32 vehicles in total, so:

$c + t = 32$ $c+t=32$

$t = 32 - c$ $t=32-c$

Now, let's use the other piece of information given in the problem (the amount of money):

$5 c + 8 t = 199$ $5c+8t=199$

$5 c + 8 (32 - c) = 199$ $5c+8(32-c)=199$

$5 c + 256 - 8 c = 199$ $5c+256-8c=199$

$256 - 199 = 8 c - 5 c$ $256-199=8c-5c$

$3 c = 57$ $3c=57$

$c = 19$ $c=19$

There are 19 cars. Therefore, the number of trucks is:

$32 - 19 = 13$ $32-19=13$ trucks

Let's check our answer:

$19 + 13 = 32$ $19+13=32$ vehicles

$19 \cdot 5 + 13 \cdot 8 = 95 + 104 = $ 199$ $19*5+13*8=95+104=$199$

It looks like our answers are correct and make sense. Hope this helps!

Answer 2 · 2017-11-20T04:53:27

Number of cars $x = 19$ $x=19$
Number of trucks $y = 3$ $y=3$

Explanation:

Given -

Rate to wash one car $= $ .5$ $=$.5$
Rate to wash one truck $= $ .8$ $=$.8$
Total Amount collected $= $ .199$ $=$.199$
Number of vehicles $= 32$ $=32$

Let -
Number of cars be $= x$ $=x$
Number of trucks $= y$ $=y$

Based on the above pieces of information, we can form two equations

$x + y = 32$ $x+y=32$ --------------(1) Total cars and trucks washed
$5 x + 8 y = 199$ $5x+8y=199$ --------------(2) Total amount collected

Solve the 1st equation for $y$ $y$

$y = 32 - x$ $y=32-x$

Substitute $y = 32 - x$ $y=32-x$ in equation (2)

$5 x + 8 (32 - x) = 199$ $5x+8(32-x)=199$

$5 x + 256 - 8 x = 199$ $5x+256-8x=199$

$5 x - 8 x = 199 - 256 = - 57$ $5x-8x=199-256=-57$
$- 3 x = - 57$ $-3x=-57$

$x = \frac{- 57}{- 3} = 19$ $x=(-57)/(-3)=19$

Substitute $x = 19$ $x=19$ in equation (1)

$19 + y = 32$ $19+y=32$
$y = 32 - 19 = 3$ $y=32-19=3$

$y = 3$ $y=3$

Number of cars $x = 19$ $x=19$
Number of trucks $y = 3$ $y=3$

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The drama club is having a car wash as a fundraiser. They wash cars for $5 each and trucks for $8 each. How many of each type of vehicle did they wash if they raised $199 by washing 32 vehicles?

2 Answers

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