Question

Pranav and Julia each improved their yards by planting grass sod and ivy. They bought their supplies from the same store. Pranav spent $196 on 12 ft² of grass sod and 13 pots of ivy. Juli spent $76 on 4 ft² of grass sod and 7 pots of ivy. Find the cost of one ft² of grass sod and of one pot of ivy.

Answer 1

The cost of one ft² of grass sod is $12 and the cost of one pot of ivy is $4.​

Step-by-step explanation:

Step 1: Define your variables:

• Let the cost of one ft² of grass sod = g

,

• Let the cost of one pot of ivy = p

Step 2: Derive the equations

Pranav spent $196 on 12 ft² of grass sod and 13 pots of ivy.

`12g+13p=196\cdots(1)`

Juli spent $76 on 4 ft² of grass sod and 7 pots of ivy.

`4g+7p=76\cdots(2)`

Step 3: Solve the system of equations

`\begin{gathered} 12g+13p=196 \\ 4g+7p=76 \end{gathered}`

Multiply the first equation by 1 and the second equation by 3:

`\begin{gathered} 12g+13p=196 \\ 12g+21p=228 \end{gathered}`

Subtract:

`\begin{gathered} 21p-13p=228-196 \\ 8p=32 \\ p=(32)/(8) \\ p=\$4 \end{gathered}`

Next, substitute p=4 to solve for g:

`\begin{gathered} 12g+13p=196 \\ 12g=196-13p \\ 12g=196-13(4) \\ 12g=144 \\ g=(144)/(12) \\ g=\$12 \end{gathered}`

The cost of one ft² of grass sod is $12 and the cost of one pot of ivy is $4.​