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?
spoons
How many spoons did the store have at the beginning of Ted's shift?
spoons
Answers
GPT-4o mini
Let \( s \) represent the number of spoons at the beginning of Ted's shift. Since there are twice as many spatulas as spoons, the number of spatulas at the beginning of the shift would be \( 2s \).
During his shift, the store sold 32 spatulas and 13 spoons. Therefore, at the end of the shift, the number of spoons and spatulas remaining can be given by the following equations:
- Remaining spoons: \( s - 13 \)
- Remaining spatulas: \( 2s - 32 \)
According to the problem, at the end of Ted's shift, the store had the same number of spoons and spatulas. We can set the equations equal to each other:
\[
s - 13 = 2s - 32
\]
Now, we can solve for \( s \):
1. Rearranging the equation gives:
\[
-13 + 32 = 2s - s
\]
\[
19 = s
\]
Thus, the number of spoons the store had at the beginning of Ted's shift was \( \boxed{19} \).
### Verification
1. Starting with \( s = 19 \):
- Number of spoons: \( 19 \)
- Number of spatulas: \( 2s = 2 \times 19 = 38 \)
2. After selling 32 spatulas and 13 spoons:
- Remaining spoons: \( 19 - 13 = 6 \)
- Remaining spatulas: \( 38 - 32 = 6 \)
Both the remaining spoons and spatulas are equal, confirming our solution is correct. The number of spoons at the beginning of Ted's shift is indeed \( \boxed{19} \).
During his shift, the store sold 32 spatulas and 13 spoons. Therefore, at the end of the shift, the number of spoons and spatulas remaining can be given by the following equations:
- Remaining spoons: \( s - 13 \)
- Remaining spatulas: \( 2s - 32 \)
According to the problem, at the end of Ted's shift, the store had the same number of spoons and spatulas. We can set the equations equal to each other:
\[
s - 13 = 2s - 32
\]
Now, we can solve for \( s \):
1. Rearranging the equation gives:
\[
-13 + 32 = 2s - s
\]
\[
19 = s
\]
Thus, the number of spoons the store had at the beginning of Ted's shift was \( \boxed{19} \).
### Verification
1. Starting with \( s = 19 \):
- Number of spoons: \( 19 \)
- Number of spatulas: \( 2s = 2 \times 19 = 38 \)
2. After selling 32 spatulas and 13 spoons:
- Remaining spoons: \( 19 - 13 = 6 \)
- Remaining spatulas: \( 38 - 32 = 6 \)
Both the remaining spoons and spatulas are equal, confirming our solution is correct. The number of spoons at the beginning of Ted's shift is indeed \( \boxed{19} \).