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]