Jim bought some potted plants:

Question

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 4 petunias.
Jim bought 4 petunias.

Jim bought 15 petunias.
Jim bought 15 petunias.

Jim bought 15 begonias.
Jim bought 15 begonias.

Jim bought 18 begonias.

Answer 1

Let's define the variables for the problem:

• Let \( p \) be the number of petunias Jim bought.
• Let \( b \) be the number of begonias Jim bought.

We know the following from the problem statement:

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

2. The total amount spent is $225: \[ 11p + 15b = 225 \]

Now, we can use these two equations to solve for \( p \) and \( b \).

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

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

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

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

Subtract 285 from both sides: \[ -4p = 225 - 285 \] \[ -4p = -60 \]

Dividing both sides by -4: \[ p = 15 \]

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

Thus, Jim bought:

• 15 petunias
• 4 begonias

Based on the provided statements:

• Jim bought 4 petunias. (Incorrect)
• Jim bought 4 petunias. (Incorrect)
• Jim bought 15 begonias. (Incorrect)
• Jim bought 18 begonias. (Incorrect)

Based on our calculations, none of the provided statements are correct. The correct conclusion is that Jim bought 15 petunias and 4 begonias.