Respuesta :
Answer:
The cost of one ft² of grass sod is $12 and the cost of one pot of ivy is $4.
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.
[tex]12g+13p=196\cdots(1)[/tex]Juli spent $76 on 4 ft² of grass sod and 7 pots of ivy.
[tex]4g+7p=76\cdots(2)[/tex]Step 3: Solve the system of equations
[tex]\begin{gathered} 12g+13p=196 \\ 4g+7p=76 \end{gathered}[/tex]Multiply the first equation by 1 and the second equation by 3:
[tex]\begin{gathered} 12g+13p=196 \\ 12g+21p=228 \end{gathered}[/tex]Subtract:
[tex]\begin{gathered} 21p-13p=228-196 \\ 8p=32 \\ p=\frac{32}{8} \\ p=\$4 \end{gathered}[/tex]Next, substitute p=4 to solve for g:
[tex]\begin{gathered} 12g+13p=196 \\ 12g=196-13p \\ 12g=196-13(4) \\ 12g=144 \\ g=\frac{144}{12} \\ g=\$12 \end{gathered}[/tex]The cost of one ft² of grass sod is $12 and the cost of one pot of ivy is $4.
