A cafe sells muffins and scones. A customer purchases 2 muffins and 1 scone for a total of… — Armed Services Vocational Aptitude Battery (ASVAB)

A cafe sells muffins and scones. A customer purchases $2$ muffins and $1$ scone for a total of $11$ dollars. If the price of one scone is $4$ dollars less than the price of $3$ muffins, what is the price of one scone in dollars?

Answer: 5 dollars

Answer

The price of one scone is

5

dollars.

By translating the word problem into a system of two equations (

2m + s = 11

and

s = 3m - 4

) and using substitution, we find that

m = 3

and

s = 5

. Thus, the price of one scone is

5

Step-by-Step Solution

Define variables and set up the equations based on the word problem.

Let

m

= price of a muffin and

s

= price of a scone. The equations are

2m + s = 11

and

s = 3m - 4

Translating the text into algebraic equations allows us to solve for the unknown values.

Substitute the expression for

s

from the second equation into the first equation.

2m + (3m - 4) = 11

This eliminates the variable

s

, leaving an equation with only one variable,

m

Solve the resulting equation for

m

5m - 4 = 11 \Rightarrow 5m = 15 \Rightarrow m = 3

Isolating

m

gives us the price of one muffin.

Substitute the value of

m

back into the equation for

s

s = 3(3) - 4 = 9 - 4 = 5

This calculates the price of the scone, which is the final requested value.

Key Concept

Solving systems of linear equations using the substitution method.

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