Example of Word Problems Involving Money:
A collection of coins consists of nickels, dimes & quarters. The number of quarters is double 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 kind 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:
$5.05 = (x)($0.05) + (x + 5)($0.10) + (2x)($0.25)
$5.05 = $0.05x + $0.10x + $0.50 + $0.50x
$5.05 = $0.65x + $0.50
$0.65x = $5.05 - $0.50
$0.65x = $4.55
x = $ 4.55/$0.65
x = 7
Solving for the other unknowns:
2x = 2(7)
2x = 14
x + 5 = 7 + 5
x + 5 = 12
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.