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Vsevolod
7 days ago
10

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?
Mathematics
2 answers:
Inessa [9K]7 days ago
8 0

The quantity of compost purchased is represented as ' C ' cubic yards.
Each cubic yard of compost is priced at $25.
Therefore, the total cost spent on compost is 25C.

The amount of topsoil acquired is ' T ' cubic yards.
The cost for each cubic yard of topsoil is $15.
Hence, the total amount spent on topsoil is 15T.

In total, the volume collected is defined by C + T = 10 cubic yards
The cost for the combined load stands at: 25C + 15T = $180

This forms the system of equations to be resolved:

C + T = 10
25C + 15T = 180.
Can you solve that?
Here’s some assistance.
If you multiply the first equation by 25 and rewrite the second below it:
25C + 25T = 250
25C + 15T = 180.
By subtracting the second from the first:[TAG_22]] 10T = 70
After dividing both sides by 10:
T = 7 cubic yards
.
Do you provide Gary with a commission? A finder's fee?
A kickback?
Inessa [9K]7 days ago
4 0

Let C denote the quantity of compost

T represent the quantity of topsoil

Each cubic yard of compost is priced at $25

Thus, the cost of C cubic yards of compost is 25C

Each cubic yard of topsoil costs $15

Therefore, the cost for T cubic yards of topsoil is 15T

Together, the amount of compost plus topsoil equals 10

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

The total cost for compost and topsoil is $180

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

Rearranging the first equation to find C

C + T = 10

results in

C = 10 - T

Now substitute into the second equation

25C + 15T = 180

25 ( 10 - T) +15T = 180

Using like terms: 250 - 25T + 15T = 180

From which we can simplify to 250 - 10T = 180 by removing 250 from both sides

-10T = 180 - 250

yielding -10T = -70 (dividing both sides by -10)

results in T = 7


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