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Jimmy and Kathryn each improved their yards by planting sod and geraniums. They bought their supplies from the same store. Jimmy spent $162 on 13 ft2 of sod, , and 12 geraniums, . Kathryn spent $126 on 7ft2 of sod and 12 geraniums. Write equations to represent the scenario. Then, find the cost of one ft2 of sod and the cost of one geranium.

Jimmy and Kathryn each improved their yards by planting sod and geraniums They bought their supplies from the same store Jimmy spent 162 on 13

Answer :

Given:

Jimmy spent $162 on 13 sqaure feet of sod and 12 geraniums.

Kathryn spent $126 on 7 square feet of sod and 12 geraniums.

Required:

We need to find the cost of one square foot of sod and the cost of one geranium.

Explanation:

Let s be the number of sqaure feet of sod.

Let g be the number geranium.

Consider that Jimmy spent $162 on 13 sqaure feet of sod and 12 geraniums.

[tex]13s+12g=162[/tex]

Consider that Kathryn spent $126 on 7 square feet of sod and 12 geraniums.

[tex]7s+12g=126[/tex]

[tex]Subtract\text{ the equation }7s+12g=126\text{ from the equation }13s+12g=162.[/tex]

[tex](13s+12g)-(7s+12g)=162-126[/tex]

[tex]13s+12g-7s-12g=36[/tex]

[tex]13s-7s+12g-12g=36[/tex]

[tex]6s=36[/tex]

Divide both sides by 6.

[tex]\frac{6s}{6}=\frac{36}{6}[/tex][tex]s=6[/tex]

[tex]Substitue\text{ }s=6\text{ in the equation 1}3s+12g=162.[/tex][tex]13(6)+12g=162[/tex]

[tex]78+12g=162[/tex]

Subtract 78 from both sides of the equation.

[tex]78+12g-78=162-78[/tex][tex]12g=84[/tex]

Divide both sides by 12.

[tex]\frac{12g}{12}=\frac{84}{12}[/tex][tex]g=7[/tex]

Final answer:

[tex]Jimmy:\text{ }13s+12g=162[/tex]

[tex]Kathryn:\text{ }7s+12g=126[/tex][tex]Square\text{ foot of sod =\$6}[/tex][tex]G\text{eranium =\$ 7.}[/tex]

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