Question

Susan bought some potted plants.

Petunias cost $7 per pot.
Begonias cost $8 per pot.
She bought 22 potted plants and spent a total of $163. How many petunias did Susan buy?

A.
7

B.
13

C.
11

D.
9

Answer 1

Let \( x \) be the number of petunias and \( y \) be the number of begonias that Susan bought. We can set up the following system of equations based on the information given:

1. The total number of plants:
\[
x + y = 22
\]

2. The total cost of the plants:
\[
7x + 8y = 163
\]

Now, we can solve this system of equations. First, let's solve the first equation for \( y \):

\[
y = 22 - x
\]

Next, we can substitute \( y \) in the second equation:

\[
7x + 8(22 - x) = 163
\]

Expanding this gives:

\[
7x + 176 - 8x = 163
\]

Combining like terms results in:

\[
-x + 176 = 163
\]

Subtracting 176 from both sides:

\[
-x = 163 - 176
\]

\[
-x = -13
\]

Multiplying both sides by -1 gives:

\[
x = 13
\]

So, Susan bought \( 13 \) petunias. To find the number of begonias, substitute \( x \) back into the equation for \( y \):

\[
y = 22 - 13 = 9
\]

Now let's verify our solution. We know Susan bought 13 petunias and 9 begonias. We need to check the cost:

\[
7(13) + 8(9) = 91 + 72 = 163
\]

Since everything checks out, the answer is:

**B. 13**