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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?

(1 point)
Responses

Jim bought 15 petunias.
Jim bought 15 petunias.

Jim bought 4 petunias.
Jim bought 4 petunias.

Jim bought 15 begonias.
Jim bought 15 begonias.

Jim bought 18 begonias.

1 answer

Let's define the number of petunias Jim bought as \( p \) and the number of begonias as \( b \).

We have two equations based on the problem:

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

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

We can solve this system step by step.

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

Now, we can substitute this expression for \( b \) into the second equation: \[ 11p + 15(19 - p) = 225 \] Expanding this gives: \[ 11p + 285 - 15p = 225 \] Combining like terms results in: \[ -4p + 285 = 225 \] Subtracting 285 from both sides: \[ -4p = 225 - 285 \] \[ -4p = -60 \] Dividing both sides by -4 gives: \[ p = 15 \]

Now, substituting \( p = 15 \) back into the equation \( b = 19 - p \) to find \( b \): \[ b = 19 - 15 = 4 \]

So, Jim bought 15 petunias and 4 begonias.

Based on the options provided, the correct statement is: Jim bought 15 petunias.