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?

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.