Algebra Word Problems: 1

How to solve a word problem:

To solve this word problem you need to find 2 unknown values, the quantity of each coin that will total the total amount of money. If we call the unknown value of the first coin X and the unknown value of the second coin Y, these are the 2 values we need to find. However, since we know the total number of coins we have, the following equation is true: Y = Total Coins - X. Therefore, if we solve for X we can easily find Y.

For example, if person has 11 coins consisting of quarters and nickels and the total amount of change is $1.75 we would start solving this word problem by letting X = the number of quarters and Y = (11 - X) = the number of nickels.

Putting this into an equation to solve for X we have:
X Quarters + Y Nickels = 1.75
25 cents * X + 5 cents Y = 1.75
25 cents * X + 5 cents * (11 - X) = 1.75

It is easier to work with whole numbers so we put all of the coins in terms of their value in cents and solve for X.
25X + 5(11 - X) = 175

Multiplying out the terms in the parentheses we get
25X + 55 - 5X = 175

Combining terms that contain X we get
20X + 55 = 175

Moving like-terms to one side of the equation we get
20X + 55 - 55 = 175 - 55
20X = 120

To reduce X by itself, we divide both sides of the equation by 20:
20X / 20 = 120 / 20
X = 6 or we have 6 quarters.

To find the number of nickels we subtract 6 from the total number of coins or we solve for Y = 11 - X = 11 - 6 = 5.

Answer: 6 quarters and 5 nickels = $1.75

If necessary, use the following table of values to solve these word problems.

Coins	Cents Value	Dollar Value
Penny	1¢	$0.01
Nickel	5¢	$0.05
Dime	10¢	$0.10
Quarter	25¢	$0.25
Half Dollar	50¢	$0.50