Question

The store where Ted works is having a sale on wooden spoons and spatulas. When his shift started, there were twice as many spatulas as spoons. During his shift, the store sold 32 spatulas and 13 spoons. At the end of Ted's shift, the store had the same number of each item.
How many spoons did the store have at the beginning of Ted's shift?

Answer 1

Let \( s \) be the number of wooden spoons at the beginning of Ted's shift. Since there were twice as many spatulas as spoons, the number of spatulas at the beginning would be \( 2s \).

During Ted's shift, the store sold 32 spatulas and 13 spoons. Therefore, the number of spoons left after the sales is:

\[
s - 13
\]

And the number of spatulas left is:

\[
2s - 32
\]

At the end of Ted's shift, it is given that the store had the same number of each item. Hence, we can set the number of remaining spoons equal to the number of remaining spatulas:

\[
s - 13 = 2s - 32
\]

Now, let's solve for \( s \). First, we'll simplify the equation:

\[
s - 13 = 2s - 32
\]

Rearranging the equation gives:

\[
-13 + 32 = 2s - s
\]

This simplifies to:

\[
19 = s
\]

Thus, the number of wooden spoons at the beginning of Ted's shift was \( \boxed{19} \).

To verify, if \( s = 19 \), then the number of spatulas is \( 2s = 38 \).

After selling 13 spoons, the remaining spoons are:

\[
19 - 13 = 6
\]

After selling 32 spatulas, the remaining spatulas are:

\[
38 - 32 = 6
\]

Since both amounts are equal, our solution is confirmed valid. Therefore, the store had \( \boxed{19} \) spoons at the beginning of Ted's shift.