We can solve this problem using a system of equations.

Define Variables:

Let:

• $x$ = number of cupcakes sold
• $y$ = number of donuts sold

Set Up Equations:

1. The total number of items sold:
   $x + y = 35$
2. The total cost of the items:
   $4.50x + 3y = 138$

Solve the System:

We solve for one variable using substitution or elimination.

Step 1: Express $y$ in terms of $x$:

From the first equation:
$y = 35 - x$

Step 2: Substitute into the second equation:

$4.50x + 3(35 - x) = 138$

Step 3: Expand and solve for $x$:

$4.50x + 105 - 3x = 138$ $1.50x + 105 = 138$ $1.50x = 33$ $x = 22$

Step 4: Find $y$:

$y = 35 - 22 = 13$

Final Answer:

• 22 cupcakes
• 13 donuts

Would you like a step-by-step verification? Let me know if you have any questions!

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Related Questions:

1. If the price of cupcakes increases to $5, how would this affect the total cost?
2. If the customer had bought 5 more items while keeping the same ratio of cupcakes to donuts, how many of each would they have bought?
3. What if the customer had spent only $120? How many cupcakes and donuts would that imply?
4. Can we generalize a formula for any total number of items and total cost?
5. What would the answer be if the prices of cupcakes and donuts were swapped?

Math Tip:

When solving a system of equations, substitution is helpful when one equation is already solved for a variable, while elimination works well if coefficients align for easy cancellation.