Question

Helena uses a mixture of compost and topsoil in her garden. She purchased a total of 10 cubic yards of compost and topsoil for $180. If compost costs $25 per cubic yard and topsoil costs $15 per cubic yard, how many cubic yards of topsoil did she purchase?

Answer 1

Amount of compost she bought = ' C ' cubic yards.
Each cubic yard of compost costs $25.
Amount she spent on compost  =  25C .

Amount of topsoil she bought = ' T ' cubic yards.
Each cubic yard of topsoil costs $15.
Amount she spent on topsoil =  15T .

Total volume she bought  =                 C + T       = 10 cubic yards
Total price for the whole truckload =  25C + 15T  =  $180

There's the system of equations you have to solve:

                                                    C +    T  =    10
                                                25C + 15T  =  180 .
Can you do that ?
Here.  Let me help.

Multiply the first equation
by 25, then write the second
one under it again:                  25C + 25T  =  250
                                                     25C + 15T  =  180 .

Subtractum:                                      10T  =  70

Divide each side by  10:                       T  =  7  cubic yards.


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Answer 2

Let C be the amount of compost

T be the amount of  topsoil

Each compost cost = $25

Cost of C compost = 25C

Each topsoil cost = $15

Cost of T topsoil = 15T

Amount of compost + amount of topsoil = 10

C + T = 10 -------> Equation 1

cost of C compost + cost of T topsoil = 180

25C + 15T = 180 --------> equation 2

Solve  the first equation for C

C + T = 10

C = 10 - T

Now plug it in second equation

25C + 15T = 180

25 ( 10 - T) +15T = 180

250 - 25T + 15T = 180 (combine like terms)

250 - 10 T = 180 (Subtract 250 on both sides)

-10T = 180 - 250

-10T = -70 ( divide by -10 on both sides)

T = 7

She purchased  7 cubic yards of topsoil .