 BenoguigoliB

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? ### Answer & Explanation Corben Pittman Skilled2021-02-01Added 83 answers 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 $\left\{5p+3s=98,s=6+p\right\}$. 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:
$5p+3s=98$
$5p+3\left(6+p\right)=98$
$5p+18+3p=98$
$8p+18=98$
$8p=80$
$p=10$
The vegetable stand then sold $p=10$ pumpkins and $s=6+p=6+10=16$ squash.

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