Question

Jim bought some potted plants: Petunias cost $11 per pot and Begonias cost $15 per pot.Jim bought 19 potted plants in all and spent a total of $225 on the plants.Which would be a correct statement?(1 point)ResponsesJim bought 4 petunias.Jim bought 4 petunias.Jim bought 15 begonias.Jim bought 15 begonias.Jim bought 18 begonias.Jim bought 18 begonias.Jim bought 15 petunias.

Answer 1

Let \( p \) be the number of petunias and \( b \) be the number of begonias.

We have the following system of equations based on the information provided:

1. \( p + b = 19 \) (equation for the total number of plants)
2. \( 11p + 15b = 225 \) (equation for the total cost)

We can solve this system to find \( p \) and \( b \).

From the first equation, we can express \( b \) in terms of \( p \):

\[ b = 19 - p \]

Now substitute \( b \) into the second equation:

\[ 11p + 15(19 - p) = 225 \]

Expanding this gives:

\[ 11p + 285 - 15p = 225 \]

Combine like terms:

\[ -4p + 285 = 225 \]

Now isolate \( p \):

\[ -4p = 225 - 285 \] \[ -4p = -60 \] \[ p = 15 \]

Now that we have \( p = 15 \), we can find \( b \):

\[ b = 19 - p = 19 - 15 = 4 \]

Thus, Jim bought 15 petunias and 4 begonias.

Looking at the provided statements:

• Jim bought 4 petunias. (False)
• Jim bought 15 begonias. (False)
• Jim bought 18 begonias. (False)
• Jim bought 15 petunias. (True)

The correct statement is: Jim bought 15 petunias.