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 teds shift, the store had the same number of each item. how many spoons did the store have at the beginning of teds shift? spoons

Explanation:

Step1: Define variables

Let the number of spoons at the start be \( x \). Then the number of spatulas at the start is \( 2x \) (since there were twice as many spatulas as spoons).

Step2: Set up equation for end quantities

After selling 32 spatulas and 13 spoons, the number of spoons left is \( x - 13 \) and the number of spatulas left is \( 2x - 32 \). Since these are equal at the end, we set up the equation:
\( 2x - 32 = x - 13 \)

Step3: Solve the equation

Subtract \( x \) from both sides: \( 2x - x - 32 = x - x - 13 \) which simplifies to \( x - 32 = -13 \).
Then add 32 to both sides: \( x - 32 + 32 = -13 + 32 \), so \( x = 19 \).

Answer:

19