Please Help. I am SO Stuck!! (Algebra)?

Question

At a school-sponsored car wash, the fees charged were : $5 per car, $8 per pickup truck and $10 per full-sized van. Twice as many cars were washed as pickup trucks. The amount collected for washing cars and pickup trucks was $360. A total of $410 was collected at the car wash.

Let c represent the number of cars washed, t represent number trucks washed, and v represent number of vans washed. Write a system of 3 equations that represents the number of vehicles washed. Find the number of cars washed.

I am mainly having a hard time figuring out how to write the system of equations. Help!!

Thanks so much!

Answer 1

The total collected was $410, which is $5 times the number of cars washed, $8 times the number of trucks washed, and $10 times the number of vans washed:

5c + 8t + 10v = 410

Twice as many cars were washed as trucks, so you'd double the number of trucks washed in order to get the number of cars:

2t = c

The amount collected for just cars and trucks ($5 per car times the number of cars and $8 per truck times the number of trucks) is $360:

5c + 8t = 360

So putting them all together it's

5c + 8t + 10v = 410
5c + 8t = 360
2t = c

There are many ways to attack solving the three equations. However, notice that two equations have 5c + 8t in them. So to get things done fast, since you know that 5c + 8t = 360, you can substitute 360 in the first equation and solve for v very easily:

(5c + 8t) + 10v = 410
360 + 10v = 410
10v = 50
v = 5

Then to get the number of trucks and cars, you can use the third equation to substitute 2c for t in the second equation:

5c + 8t = 360
5(2t) + 8t = 360
10t + 8t = 360
18t = 360
t = 20

And then finally, you know that twice as many cars were washed as trucks, so c = 40.

40 cars, 20 trucks, and 5 vans.

To check:

$5(40) + $8(20) + 5($10) = $200 + $160 + $50 = $410

So it's correct.

Answer 2

40 cars, 20 trucks and 5 vans.

First the vans. The total collected was $410 and the amount for cars and trucks was $360. The difference was the vans. So the difference divided by the cost per van yields the number of cans: ($410 - $360) / $10/van = $50/$10 vans = 5 vans. In equation form, that was: {($5*c + $8*t + $10*v) - ($5*c + $8*t)} / $10.

Next, the cars and trucks. Twice as many cars were done as trucks and they earned $360 between them so the equations are: 2*t = c and $5*c + $8*t = $360. Substitute 2t for the c in the second equation and cancel out the dollar signs: 5*(2t) + 8t = 360 so: 18t = 360 and t = 360/18 = 20 trucks. Substitute back into either equation and: 2*20 = c = 40 cars.

Answer 3

Here's the key to understanding the solution:
if c is the number of cars washed, and its 5 bucks per car, then 5 times c is the amount collected for total cars washed. got it?

so:
$5c is $ collected for cars
$8t is $ collected for trucks
$10v is $ collected for vans

but:
twice as many cars were washed as trucks, so:
c=2t ... [if, for example, 3 trucks were washed, then 6 cars were washed]

therefore we may replace c by 2t [ or t by c/2] and get:
$10t is $ collected for cars

now we have:
$10t + $8t = $360
$10t + $8t + $10v = $450

solving the top equation first:
18t=360
t=20

since t=20, then c=2t=40

the second equation:
we know that 10t+8t = 360, so
$360 + $10v = $410
10v = 50
v=5

but since the question is find the number of cars washed, the answer is 40.

to check, plug back in:
40(5) + 20(8) + 5(10) = 410
200 +160 + 50 = 410
410 = 410

just set up you problems a lttile bit at a time using each fact and you'll get it

Answer 4

c=2t
5c+8t=360
5c+8t+10v=410
5c+8t=360 subtract
10v=50
v= 5 vans
5(2t)+8t=360
10t+8t=360
18t=360
t=20 trucks
c=2t=2*20=40 cars
check
5*40+8*20+10*5=200+160+50=410

5 vans
20 trucks
40 cars

Answer 5

5c+8t+10v=410 (1)
2t=c (2)
5c+8t=360 (3)

(1)(3) => 10v=50 => v=5
(2) => 8t=4c (4)
(3)(4) => 9c=360 => c=40 (5)
(5)(2) => t=20

c=40, t=20, v=5

Answer 6

5c + 8t + 10v = 410

2t = c

5c + 8t = 360

Answer 7

5c + 8t + 10v = 410
5c + 8t = 360
2t = c

Answer 8

Here is what I think the equations would be:

c=2t
c+t=360
v+c+t=410

Of course we know:
v=5
t=20
c=40

Hope this helps.