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?

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?

Question
Systems of equations
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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