Heather and Carlos each improved their yards by planting grass sod and geraniums. They bought their supplies from the same store. Heather spent $171 on 14ft^2 of grass sod and 5 geraniums. Carlos spent $117 on 6ft^2 of grass sod and 7 geraniums. Find the cost of one ft^2 of grass sod and the cost of one geranium.

The cost of one ft^2 of grass sod = $9

the cost of one geranium= $9

Step-by-step explanation:

Hi, to answer this question we have to write a cost equation for each one:

Heather : 14x+5y =171

Carlos: 6x+7y=117

Where x is the cost of one ft^2 of grass sod and y is the cost of one geranium.

Multiplying Heather's equation by 7, Carlos' equation by 5, and subtracting Carlos' cost to Heather's cost:

98x+35y=1,197

-

30x+35y=585

68x=612

Solving for x:

x = 612/68

x=$9 per ft2

Replacing x=9 on any equation:

6(9)+7y=117

54+7y=117

7y=117-54

7y=63

y=63/7

y=$9  

answ9x x 3=

step-by-step explanation:

answer: yes, since the line has a steeper rate of change than the exponential the y-values will be greater and they will only intersect one time.