# Solving a Problem Involving Prices

Solving a Problem Involving Prices

At Panera Bread, a loaf of honey wheat bread costs 2.99, and a loaf of French bread costs 66.07. How many loaves of each type of bread were sold? (Source: Panera Bread menu.)

Step 1:-  Read the problem again. There are three unknowns in this problem.

Step 2:-  Assign variables to represent the three unknowns.

Let x = the number of loaves of honey wheat,

y = the number of loaves of sunflower,

and z = the number of loaves of French bread.

Step 3:-  Write a system of three equations. Since three times as many

loaves of honey wheat were sold as sunflower,

x = 3y , or x – 3y = 0. (1)

Also,

Number of loaves of French bread = z

equals =

5 less than the number of loaves of honey wheat.

So

x – z = 5. (2)

multiplying the cost of a loaf of a each kind of bread by  the number of loaves of that kind sold adding gives the total receipt.

2.59x + 2.99y + 3.29z = 66.07

Multiply each side of this equation by 100 to clear it of decimals.

259x + 299y + 329z = 6607 (3)

Step 4:-  Solve the system of three equations .

Step 5:-  State the answer. The solution set is {(12, 4, 7)}, meaning that 12 loaves of honey wheat, 4 loaves of sunflower, and 7 loaves of French bread were sold.

Step 6:-  Check. Since 12 = 3 .4, the number of loaves of honey wheat is three times the number of loaves of sunflower. Also, 12 – 7 = 5, so the number of loaves of French bread is 5 less than the number of loaves of honey wheat. Multiply the appropriate cost per loaf by the

number of loaves sold and add the results to check that total receipts were \$66.07.