Question

A roadside vegetable stand sells pumpkins for $5 each and squashes for $3 each. One day they sold 6 more squash than pumpkins, and their sales totaled $98. Write and solve a system of equations to find how many pumpkins and quash they sold?

Systems of equations
ANSWERED
asked 2021-01-31
A roadside vegetable stand sells pumpkins for $5 each and squashes for $3 each. One day they sold 6 more squash than pumpkins, and their sales totaled $98. Write and solve a system of equations to find how many pumpkins and quash they sold?

Answers (1)

2021-02-01

Let p be the number of pumpkins and ss be the number of squash they sold.
Since they sell each pumpkin for $5, they will earn 5p dollars selling pp pumpkins. Since they sell each squash for $3, they will earn 3s dollars selling ss squash. The total amount they will earn is then \(5p+3s\). If their sales totaled $98, then \(5p+3s=98\).
If they sold 6 more squash than pumpkins, then the number of squash they sold, s, is 6 more than the number of pumpkins they sold, p. This gives the equation \(s=6+p\).
You then have the system \(\{5p+3s=98,s=6+p\}\). Since the second equation is already solved for p you should use the substitution method to solve.
Substitute \(s=6+p\) into \(5p+3s=98\) and solve for p:
\(5p+3s=98\)
\(5p+3(6+p)=98\)
\(5p+18+3p=98\)
\(8p+18=98\)
\(8p=80\)
\(p=10\)
The vegetable stand then sold \(p=10\) pumpkins and \(s=6+p=6+10=16\) squash.

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