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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.

1 answer

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."