12. Corinne's pumpkin weighs 28 ounces and is growing at a rate of 5 ounces per week. Ron's pumpkin weighs 10 ounces and is growing at a rate of 13 ounces per week. Let t represent time in weeks and $$ w $$ represent weight in ounces. Which system of equations can be used to determine when the weights of the two pumpkins will be equal? $$ \begin{array}{ll} ext { (A) }\left\{\begin{array}{l}w=5+28 t \ w=13+10 t\end{array} ight. \ \begin{array}{ll}w=5 t-28\end{array} \ ext { (B) }\left\{\begin{array}{l}w=5(t+28) \ w=13(t+10)\end{array} ight. & ext { (D) }\left\{\begin{array}{l}w=5 t+28 \ w=13 t-10\end{array} ight. \ w=13 t+10\end{array} $$

Question

12. Corinne's pumpkin weighs 28 ounces and is growing at a rate of 5 ounces per week. Ron's pumpkin weighs 10 ounces and is growing at a rate of 13 ounces per week. Let t represent time in weeks and $$ w $$ represent weight in ounces. Which system of equations can be used to determine when the weights of the two pumpkins will be equal? $$ \begin{array}{ll}	ext { (A) }\left\{\begin{array}{l}w=5+28 t \ w=13+10 t\end{array}ight. \ \begin{array}{ll}w=5 t-28\end{array} \ 	ext { (B) }\left\{\begin{array}{l}w=5(t+28) \ w=13(t+10)\end{array}ight. & 	ext { (D) }\left\{\begin{array}{l}w=5 t+28 \ w=13 t-10\end{array}ight. \ w=13 t+10\end{array} $$

UpStudy AI · Accepted Answer

To determine when the weights of Corinne's and Ron's pumpkins will be equal, we need to set up a system of equations based on the information provided.

1. **Corinne's pumpkin:**
   - Initial weight: 28 ounces
   - Growth rate: 5 ounces per week
   - Weight after $$ t $$ weeks: 
     $$
     w = 5t + 28
     $$

2. **Ron's pumpkin:**
   - Initial weight: 10 ounces
   - Growth rate: 13 ounces per week
   - Weight after $$ t $$ weeks: 
     $$
     w = 13t + 10
     $$

Now, we can set up the system of equations to find when the weights are equal:
$$
\begin{cases}
w = 5t + 28 \
w = 13t + 10
\end{cases}
$$

This corresponds to option (D):
$$
\begin{cases}
w = 5t + 28 \
w = 13t + 10
\end{cases}
$$

Thus, the correct system of equations is:
$$
\begin{cases}
w = 5t + 28 \
w = 13t + 10
\end{cases}
$$
The correct system of equations is: $$ \begin{cases} w = 5t + 28 \ w = 13t + 10 \end{cases} $$

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