A vegetable stand sells $p$ pumpkins for $\$ 5.00$ each and $s$ squashes for $\$ 3.00$ each. On Monday, the stand sold $6$ more squashes than pumpkins and made a total of $\$ 98.00$ . Which system of equations can be used to determine the number of pumpkins and squashes sold? $\newline$ Choose $1$ answer: $\newline$ (A) $3 p+5 s=98$ $\newline$ $s=p+6$ $\newline$ (B) $3 p+5 s=98$ $\newline$ $p=s+6$ $\newline$ (C) $5 p+3 s=98$ $\newline$ $s=p+6$ $\newline$ (D) $5 p+3 s=98$ $\newline$ $p=s+6$

Full solution

Q. A vegetable stand sells

p

pumpkins for

\$ 5.00

each and

s

squashes for

\$ 3.00

each. On Monday, the stand sold

6

more squashes than pumpkins and made a total of

\$ 98.00

. Which system of equations can be used to determine the number of pumpkins and squashes sold?

\newline

Choose

1

answer:

\newline

(A)

3 p+5 s=98

\newline

s=p+6

\newline

(B)

3 p+5 s=98

\newline

p=s+6

\newline

(C)

5 p+3 s=98

\newline

s=p+6

\newline

(D)

5 p+3 s=98

\newline

p=s+6

Identify Equations: question_prompt: What system of equations can be used to determine the number of pumpkins ( extit{p}) and squashes ( extit{s}) sold if the stand sold $6$ more squashes than pumpkins and made a total of $\$98.00$ ?
Write Total Money Equation: Step $1$ : Let's write the equation for the total money made from selling pumpkins and squashes. Pumpkins cost $\$5$ each, and squashes cost $\$3$ each. So, the equation is: $\newline$ $5p + 3s = 98$
Establish Relationship Equation: Step $2$ : Now, we know that the stand sold $6$ more squashes than pumpkins. So, the equation for the relationship between the number of squashes and pumpkins sold is: $\newline$ $s = p + 6$
Compare with Options: Step $3$ : We need to check which answer choice matches our equations. Let's look at the options: $\newline$ (A) $3p + 5s = 98$ , $s = p + 6$ $\newline$ (B) $3p + 5s = 98$ , $p = s + 6$ $\newline$ (C) $5p + 3s = 98$ , $s = p + 6$ $\newline$ (D) $5p + 3s = 98$ , $p = s + $6$
Compare with Options: Step $3$: We need to check which answer choice matches our equations. Let's look at the options:$\newline$(A) $3p + 5s = 98$, $s = p + 6$$\newline$(B) $3p + 5s = 98$, $p = s + 6$$\newline$(C) $5p + 3s = 98$, $s = p + 6$$\newline$(D) $5p + 3s = 98$, $p = s + 6$ Step $4$: By comparing the equations we wrote with the options, we can see that option (C) has the same equations as we derived:$\newline$$5p + 3s = 98$, $s = p + 6$