Question

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 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.