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?

Jim bought 18 begonias.

Jim bought 4 petunias.

Jim bought 15 begonias.

Jim bought 15 petunias.

Answer 1

Let \( p \) represent the number of petunias and \( b \) represent the number of begonias. We have the following system of equations based on the information provided:

1. The total number of plants purchased:
\[
p + b = 19
\]

2. The total cost of the plants:
\[
11p + 15b = 225
\]

Now we can solve this system of equations.

From the first equation, we can express \( b \) in terms of \( p \):
\[
b = 19 - p
\]

Next, we substitute \( b \) in the second equation:
\[
11p + 15(19 - p) = 225
\]
Expanding this, we get:
\[
11p + 285 - 15p = 225
\]

Combining like terms results in:
\[
-4p + 285 = 225
\]

Now, we isolate \( p \):
\[
-4p = 225 - 285
\]
\[
-4p = -60
\]
\[
p = 15
\]

Now that we have \( p \), we can find \( b \):
\[
b = 19 - p = 19 - 15 = 4
\]

So, Jim bought 15 petunias and 4 begonias.

The correct statement based on this information is:
- "Jim bought 15 petunias."