Math word problem!!! helpp?

Question

I can't figure this out:

the math problem reads:

The math club wated to raise money for its summer trip. They charged $3 for each car and $5 for each truck. If they washed 49 vehicles and earned $181, how many of each kind of vehicle did they wash?

how do you figure it out? can yu do step-by-step? thank you

Answer 1

Let c be the number of cars, and t the number of trucks. You know:

c + t = 49 (49 total vehicles)
3c + 5t = 181 ($3/car plus $5/truck = $181)

Solve the first equation for c and substitute into the second:

c + t = 49
c = 49 - t

3c + 5t = 181
3(49 - t) + 5t = 181
147 - 3t + 5t = 181
2t = 34
t = 17

Now you can go back to the original equation and compute the number of cars:

c + t = 49
c + 17 = 49
c = 32

And you can check with the money equation:

3c + 5t =? 181
3(32) + 5(17) =? 181
96 + 85 =? 181
181 = 181

Answer 2

Let c=car and t=truck
First equation:
c + t = 49
2nd equation
3c + 5t = 181.

Use either substitution or addition method to solve.
I will use addition method.

-3(c+t=49) or 1st equation
-3c-3t=-147 (still 1st equation)
3c+5t=181 (2nd equation), now add the two equations.
2t=34
t=17
so c must =32 if they washed 49 vehicles.
Check 2nd equation.
3*32 + 5*15= $181

Answer 3

Let x = number of cars & y = number of trucks.

3x + 5y = 181 This is how much they charged.
x + y = 49 This is how many vehicles there were.

x = 49 - y
Solve for x, then substitute into the 1st equation.
3(49-y) + 5y = 181
147 - 3y + 5y = 181
147 + 2y = 181
2y = 34
y = 17
Now that you know y, you can solve for x.
x = 49 - 17
x = 32

The club washed 32 cars and 17 trucks.

Answer 4

Total # of vehicles:
c + t = 49
c = 49 - t

Total amount of money:
3c + 5t = 181
Substitute (49 - t) for c & solve for t:
3(49 - t) + 5t = 181
147 - 3t + 5t = 181
2t = 34
t = 17
Solve for c, by substituting 17 for t:
c + 17 = 49
c = 32
There were 32 cars & 17 trucks.

Answer 5

Set it up like so:

1) 3c + 5t = 181
2) c + t = 49

from 2) we can get:

c = 49 - t

and plug it into 1)

3(49 - t) +5t = 181

147 + 2t = 181

2t = 34

t = 17

Now plug this back into 2)

c + 17 = 49

c = 32

Answer 6

Let 'c' represent cars
Let 't' represent trucks

Use substitution.

c + t = 181
3c + 5t = 49

3c = 49 - 5t

c = (49/3) - (5/3)t

Answer 7

c = number ofcars, t= number of trucks.
c+t=49........................(1)
3c+4t=181.................................(2)
4*(1)gives
4c+4t=196....................................(3)
)3-(2 gives)_
c=15, t=34