Intermediate Algebra (11th edition)

Solving a Problem Involving Prices

At Panera Bread, a loaf of honey wheat bread costs

$2.95, a loaf of sunflower bread costs $2.99, and a loaf

of French bread costs $5.79. On a recent day, three

times as many loaves of honey wheat bread were sold

as sunflower bread. The number of loaves of French

bread sold was 5 less than the number of loaves of

honey wheat bread sold. Total receipts for these

breads were $87.89. How many loaves of each type of

bread were sold? (Source:Panera Bread menu.)

Step 1 Readthe problem again. There are three unknowns in this problem.

Step 2 Assign variablesto represent the three unknowns.

Let the number of loaves of honey wheat bread,

the number of loaves of sunflower bread,

and the number of loaves of French bread.

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

honey wheat bread were sold as sunflower bread,

or Subtract 3y. (1)

Also, we have the information needed for another equation.

x= 3 y, x- 3 y= 0.

z=

y=

x=

EXAMPLE 5

SECTION 4.3 Applications of Systems of Linear Equations 239

NOW TRY
EXERCISE 5
At a concession stand, a bottle
of Gatorade costs $2.00, a
pretzel costs $1.50, and candy
items cost $1.00. Workers sold
four times as many pretzels as
candy items. The number of
Gatorades sold exceeded the
number of pretzels sold by

310. Sales for these items to-
     taled $1520. How many of
     each item was sold?

Number of loaves

of French equals

5 less than the number

of loaves of honey wheat.

Subtract x.

Multiply by (2)

Multiplying the cost of a loaf of each kind of bread by the number of loaves

of that kind sold and adding gives the total receipts.

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

(3)

Step 4 Solvethe system of three equations.

(1)

(2)

(3)

Using the method shown in Section 4.2,we will find that

and

Step 5 State the answer.The solution set is , meaning that 12 loaves

of honey wheat bread, 4 loaves of sunflower bread, and 7 loaves of French

bread were sold.

Step 6 Check.Since the number of loaves of honey wheat bread is three

times the number of loaves of sunflower bread. Also, so the

number of loaves of French bread is 5 less than the number of loaves of honey

wheat bread. Multiply the appropriate cost per loaf by the number of loaves

sold and add the results to check that total receipts were $87.89.

12 - 7 =5,

12 = 3 #4,

51 12, 4, 7 26

z= 7.

x=12,y= 4,

295 x+ 299 y+ 579 z= 8789

x-z= 5

x- 3 y= 0

295 x+ 299 y+ 579 z= 8789

2.95x+ 2.99y+5.79z =87.89

x-z= 5 - 1.

- x+z=- 5

z = x- 5

NOW TRY

NOW TRY ANSWER

5. 60 candy items, 240 pretzels,
   550 bottles of Gatorade