Question

Dan spent $40 on 5 ft² of grass sod and 10 shrubs, while Imani spent $62 on 13 ft² of grass sod and 5 shrubs. What is the cost of one ft² of grass sod and the cost of one shrub?

A) $2 per ft² of grass sod and $4 per shrub
B) $4 per ft² of grass sod and $2 per shrub
C) $6 per ft² of grass sod and $3 per shrub
D) $8 per ft² of grass sod and $5 per shrub

Answer 1

By setting up a system of linear equations based on the purchases of grass sod and shrubs and attempting to solve for the cost of each, we determined that none of the provided answer options are correct, as the cost of a shrub cannot be negative.

Step-by-step explanation:

The question requires us to solve a system of two linear equations to find the cost of one ft² of grass sod and the cost of one shrub. We can represent the cost of sod per ft² as s and the cost of a shrub as r. Two purchases are described, leading to the equations:

• 5s + 10r = 40
• 13s + 5r = 62

We can solve these equations using either the substitution or elimination method. If we multiply the first equation by 5 to eliminate the shrubs term, we get:

• 25s + 50r = 200
• 13s + 5r = 62

Subtracting the second equation from the first, we get 12s = 138, so s = 11.50. Using the value of s in the first equation, we get 5(11.50) + 10r = 40, which simplifies to 57.50 + 10r = 40. Subtracting 57.50 from both sides, we get 10r = -17.50, which is not possible since the cost cannot be negative. So, none of the provided options A) through D) are correct.