Question

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.

Answer 1

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.

Step-by-step 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.

`13s+12g=162`

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

`7s+12g=126`

`Subtract\text{ the equation }7s+12g=126\text{ from the equation }13s+12g=162.`

`(13s+12g)-(7s+12g)=162-126`

`13s+12g-7s-12g=36`

`13s-7s+12g-12g=36`

`6s=36`

Divide both sides by 6.

`(6s)/(6)=(36)/(6)`
`s=6`

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

`78+12g=162`

Subtract 78 from both sides of the equation.

`78+12g-78=162-78`
`12g=84`

Divide both sides by 12.

`(12g)/(12)=(84)/(12)`
`g=7`

Final answer:

`Jimmy:\text{ }13s+12g=162`

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