A bakery sells blueberry muffins for 3 each and chocolate chip muffins for 4 each. On Satu… — GMAT

A bakery sells blueberry muffins for $3 each and chocolate chip muffins for$ 4 each. On Saturday, the bakery sold a total of 50 muffins for $170. How many chocolate chip muffins were sold on Saturday?

Answer: 20

Answer

The bakery sold 20 chocolate chip muffins on Saturday.

Let

b

represent the number of blueberry muffins and

c

represent the number of chocolate chip muffins sold. Based on the problem text, we construct the system of equations:

b + c = 50

and

3b + 4c = 170

. From the first equation,

b = 50 - c

. Substituting this into the second equation yields

3(50 - c) + 4c = 170

, which expands to

150 - 3c + 4c = 170

. Simplifying gives

150 + c = 170

, so

c = 20

Step-by-Step Solution

Define variables and set up the system of linear equations.

b + c = 50

and

3b + 4c = 170

The total number of muffins sold is 50, and the total revenue from selling blueberry muffins at

3 each and chocolate chip muffins at

4 each is $170.

Substitute

b = 50 - c

into the cost equation.

3(50 - c) + 4c = 170 \implies 150 + c = 170

Substituting

b

in terms of

c

creates a single-variable linear equation for

c

Solve for

c

c = 20

Subtracting 150 from both sides gives the exact number of chocolate chip muffins sold.

Key Concept

Solving Systems of Linear Equations by Substitution or Elimination

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