If 3ft^2 of grass and 4 shrubs is $46, and 7ft^2 of grass and 4 shrubs is $54, what are the unit prices?

Question

Jack and Jaidee bought supplies from the same store. Jack spent $46 on 3 ft² of grass sod and 4 shrubs. Jaidee spent $54 on 7 ft² of grass sod and 4 shrubs. Find the cost of one ft² of grass sod and the cost of one shrub.

Answer 1

Call g square feet of grass and s shrubs.

3g + 4s = 46

7g + 4s = 54

Subtract the first equation from the second: 4g = 8

g = 2

Substitute that back into either equation.

3(2) + 4s = 46

6 + 4s = 46

4s = 40

s = 40/4 = 10

1 sq foot of grass is $2, and 1 shrub is $10.

Answer 2

There are plenty more problems like this (systems of equations) in Wyzant's Ask An Expert archives. Suggest you check out a few to see how they work!

G = cost/ft² of grass; S = cost/shrub.

(1) For Jack: 3G + 4S = $46

(2) For Jaidee: 7G + 4S = $54 Suggest using elimination method to get rid of S terms. (Subtract)

-4G = -$8, so G = $2/ft²

Then 3(2) + 4S = 46

4S = 40, S = $10/shrub

Check:

3(2) + 4(10) = 46

7(2) + 4(10) = 54