Find the cost of one ft2 of grass sod and the cost of one bunch of ornamental grass.

Question

Aliyah and Rob each improved their yards by planting grass sod and ornamental grass. They bought their supplies from the same store. Aliyah spent $74 on 4 ft2 of grass sod and 6 bunches of ornamental grass. Rob spent $77 on 11 ft2 of grass sod and 5 bunches of ornamental grass. Find the cost of one ft2 of grass sod and the cost of one bunch of ornamental grass. 

We need to find out what x and y represents and the system of equations.

Answer 1

x=sod and y=ornamental

4x+6y=74

11x+5y=77

4 does not go into 11 nor does 5 go into 6, so we need to multiply both rows.

Multiply the top row by -5 and the bottom row by 6

-20x-30y=-370

66x+30y=462

Add together

46x=92

Divide to get x=2

Now, equation 1 becomes

4(2)+6y=74

8 + 6y=74

6y=66

y=11

Check with equation 2

11(2)+5(11)=77

22+55=77, and it checks,

(x,y)=(2,11) ■