im 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?

(1 point)
Responses

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

To solve this problem, we can use a system of equations based on the information provided.

Let:

• \( p \) = number of petunias
• \( b \) = number of begonias

We have two equations based on the total number of plants and the total cost:

1. \( p + b = 19 \) (total number of plants)
2. \( 11p + 15b = 225 \) (total cost)

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 this 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, substituting back to find \( b \):

\[ b = 19 - p = 19 - 15 = 4 \]

So, Jim bought 15 petunias and 4 begonias.

Now let's check the cost to make sure it adds up:

Cost for petunias: \( 15 \times 11 = 165 \)
Cost for begonias: \( 4 \times 15 = 60 \)
Total cost: \( 165 + 60 = 225 \)

This is correct.

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