Question

ex 3: steve spent $33 on eating utensils. spoons cost $4 and forks cost $3. he bought a total of 9 utensils. how many of each kind did he buy?

Explanation:

Step1: Define variables

Let \( x \) be the number of spoons and \( y \) be the number of forks. We know two equations: the total number of utensils is 9, so \( x + y = 9 \), and the total cost is 33, so \( 4x + 3y = 33 \).

Step2: Solve the system of equations

From the first equation, we can express \( y \) as \( y = 9 - x \). Substitute this into the second equation:
\( 4x + 3(9 - x) = 33 \)
\( 4x + 27 - 3x = 33 \)
\( x + 27 = 33 \)
\( x = 33 - 27 = 6 \)

Step3: Find the number of forks

Substitute \( x = 6 \) into \( y = 9 - x \):
\( y = 9 - 6 = 3 \)

Answer:

He bought 6 spoons and 3 forks.