What's the cost of a loaf of bread?

Question

The cost of 4 rolls, 6 muffins, and 3 loaves of bread is $9.10. The cost of 2 rolls, 3 muffins, and a loaf of bread is $3.90. What's the cost of a loaf of bread?

Answer 1

Assign variables for the cost of one roll, one muffin, and one loaf of bread.

 

Let a = cost of one roll

Let b = cost of one muffin

Let c = cost of one loaf of bread

 

Using these variables, we can write an equation or total cost in each part of the problem description.

 

4a + 6b + 3c = 9.10                eq1

2a + 3b +  c = 3.90                 eq2

 

 

We have a system of equations.  We can use either the substitution or elimination method to solve for c.  The goal is to get an equation that is only in terms of c, because we want to find the cost of a loaf of bread.

 

We can multiply eq2 by 2 and keep eq1 as it is.  By doing so, we have 2 equations in which the coefficient of a and b are the same.

 

4a + 6b + 3c = 9.10                  eq1

4a + 6b + 2c = 7.80                  eq2

 

 

Subtract eq2 from eq1 to eliminate the a and b terms.

 

c = 1.30

 

 

The cost of a loaf of bread is then $1.30