The five basic steps for solving algebraic word problems can be used for solving word problems involving money. Writing algebraic expressions for these problems depends on the general relationship between the total value and the unit value of money. The total value of a collection of money or a collection of items with a certain monetary value equals the sum of the numbers of items each multiplied by their unit values. Thus, the total value of five pennies, three nickels, four dimes, and two quarters is found by solving the following equation:

x = 5($0.01) + 3($0.05) + 4($.10) + 2($0.25)

x=$0.05+$0.15+$0.40+$0.50

x=$1.10

The total value of 25 tickets worth $1.50 each and 30 tickets worth $0.75 each is 25($1.50) + 30($0.75) which equals $37.50 + $22.50 or $60.00. Algebraic word problems involving money are solved using this general relationship following the same five basic steps for solving any algebraic word problems.

Example 1:

The promoter of a track meet engages a 6,000 seat armory. He wants to gross $15,000. The price of children's tickets is to be one-half the price of adults' tickets. If one-third of the crowd is children, what should be the price of tickets, assuming capacity attendance?

Solution:

Step 1.Let x = Price of an Adult Ticket (in dollars)

Step 2.Then,

Step 3.Gross Income = (Number of Children's Tickets times their Unit Price) + (Number of Adults' Tickets times their Unit Price)

Step 4.Solving for x:

solving for the other unknown:

= Price of a Child's Ticket (in dollars)

Answers:

Price of Adults' Tickets = $3.00

Price of Children's Tickets = $1.50

Step 5.The price of children's tickets is one-half the price of adults' tickets.

The gross is $15,000.

4,000($3.00) + 2,000($1.50) = $12,000 + $3,000 = $15,000

Thus, the answers check.

Example 2:

A collection of coins consists of nickels, dimes, and quarters. The number of quarters is twice the number of nickels, and the number of dimes is five more than the number of nickels. If the total amount of money is $5.05, how many of each type of coin are in the collection?

Solution:

Step 1.Let x = Number of Nickels

Step 2.Then,

2x = Number of Quarters

x + 5 = Number of Dimes

Step 3.Total Value = (Number of Nickels)(Value of a Nickel) + (Number of Dimes)(Value of a Dime) + (Number of Quarters)(Value of a Quarter)

$5.05 = (x)($0.05) + (x + 5)($0.10) + (2x)($0.25)

Step 4.Solving for x:

Solving for the other unknowns:

Answers:

Number of Nickels = 7

Number of Dimes = 12

Number of Quarters = 14

Step 5. The number of quarters is twice the number of nickels.

2(7) = 14

The number of dimes is five more than the number of nickels.

7+5=12

The total value is $5.05.

7($0.05) + 12($0.10) + 14($0.25) =

$0.35 + $1.20 + $3.50 = $5.05

Thus, the answers check.