Question

Mr. Ellis has started a vegetable garden. He bought 15 bags of soil and 3 bags offertilizer for $282.72. He realized he didn't have enough supplies, so he boughtanother 5 bags of soil and 2 bags of fertilizer for $107.23. What was the cost of eachbag of soil and fertilizer? Let the cost of each bag of soil = x and the cost of eachbag of fertilizer = y. A. Each bag of soil was $12.99, and each bag of fertilizer was $16.25.B. Each bag of fertilizer was $9.75, and each bag of soil was $77.99.C. Each bag of soil was $9.75, and each bag of fertilizer was $77.99.D. Each bag of fertilizer was $12.99, and each bag of soil was $16.25.

Answer 1

The variables are:

x: cost of each bag of soil

y: cost of each bag of fertilizer

He bought 15 bags of soil and 3 bags of fertilizer for $282.72, that is,

15x + 3y = 282.72 (eq. 1)

He bought another 5 bags of soil and 2 bags of fertilizer for $107.23, that is,

5x + 2y = 107.23 (eq. 2)

Multiplying equation 2 by 3, we get:

3(5x + 2y) = 3(107.23)

3(5x) + 3(2y) = 3(107.23)

15x + 6y = 321.69 (eq. 3)

Subtracting equation 3 to equation 1, we get:

15x + 3y = 282.72

-

15x + 6y = 321.69

-------------------------------

-3y = -38.97

y = -38.97/-3

y = 12.99

Replacing this result into the first equation,

15x + 3(12.99) = 282.72

15x + 38.97 = 282.72

15x = 282.72 - 38.97

15x = 243.75

x = 243.75/15

x = 16.25

D. Each bag of fertilizer was $12.99, and each bag of soil was $16.25.