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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 18 begonias.
Jim bought 18 begonias.

Jim bought 15 begonias.
Jim bought 15 begonias.

Jim bought 15 petunias.
Jim bought 15 petunias.

Jim bought 4 petunias.

1 answer

To solve the problem, let's define the number of petunias Jim bought as \( p \) and the number of begonias as \( b \). We have the following two equations based on the information provided:

  1. The total number of plants:
    \( p + b = 19 \)

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

Now we can solve these equations step-by-step.

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

Now, we can substitute \( b \) into the second equation: \[ 11p + 15(19 - p) = 225 \]

Expanding this gives: \[ 11p + 285 - 15p = 225 \]

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

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

Now, substitute \( p \) back into the equation for \( b \): \[ b = 19 - p = 19 - 15 = 4 \]

So Jim bought:

  • 15 petunias
  • 4 begonias

Thus, the correct statement is: Jim bought 15 petunias.