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Math Word Problems - GED, PSAT, SAT, ACT, GRE Preparation
6.8 Word Problems - Coins

Example:
Jill has 26 coins in her purse. They are all dollar and quarter coins. If they add up to $18.50. How many of each coin does she have.
Solution:
Let 'd' stand for the number of dollar coins and 'q' stand for the number of quarters.
The rest of the coins are quarters.
Jill has 26 coins in her purse. They are all dollar and quarter coins. Then d + q = 26
1 dollar = 100 cents
1 quarter = 25 cents
If they add up to $18.50. Therefore 100d + 25q = 1850
Solving two equations we have
d + q = 26 -------------- equation 1
100d + 25q = 1850 ----- equation 2
d + q = 26
q = 26 - d
substituting q in equation 2
100d + 25(26 - d) = 1850
100d + 650 - 25d = 1850
75d = 1850 - 650
75d = 1200
d = 1200/75 = 16
q = 26 - d = 26 - 16 = 10
Jill has 16 dollar coins and 10 quarter coins in her purse.

Example:
There are 33 coins. They are nickels, dimes and quarters. They total to a value of $3.30. If there are three times as many nickels as quarters, and one-half as many dimes as nickels. How many coins of each kind are there?
Solution:
Let 'n' stand for number of nickels, 'd' stand for number of dimes and 'q' for the number of quarters.
Then n + d + q = 33
n = 3q
d = 0.5n = 0.5(3q) = 1.5q
substituting n and d in the equation n + d + q = 33
3q + 1.5q + q = 33
5.5q = 33
q = 6
n = 3q = 3 x 6 = 18
d = 1.5q = 1.5 x 6 = 9
There are 6 quarters 18 nickles and 9 dimes.

Example:
A box contain the same number of pennies, nickels and dimes. The coins total $1.44. How many of each type of coin does the box contain?
Solution:
Let 'p' stand for number of pennies, 'n' stand for number of nickles and 'd' stand for number of dimes.
There are equal number of each of these implies that
number of pennies is p, number of nickles is p and number of dimes is p
The value of the coin is the number of cents for each coin times the number of that type of coin, therefore
value of pennies = 1p
value of nickles = 5p
value of dimes = 10p
The total value is $1.44
Therefore 1p + 5p + 10p = 144
16p = 144
p = 9
q = 9
d = 9
There are 9 of each type of coin in the box.

Directions: Solve the following word problems.
Q 1: Peter has three times as many one-dollar bills as he does five dollar bills. He has a total of $32. How many of each bill does she have?
3 ones and 12 fives
2 ones and 6 fives
12 ones and 4 fives

Q 2: Sam has 30 coins, quarters and dimes, which total $5.70. How many of each does she have?(Hint: Let d be the number of dimes and q be number of quarters. Then the equations can be written as d + q = 30 and 10d + 25q = 570. Solve for d and q.)
quarters = 18 and dimes = 12
quarters = 18 and dimes = 10
quarters = 16 and dimes = 15

Q 3: Tom has 7 more quarters than dimes and has a total of $6.80. The number of quarters and dimes is 38. How many quarters and dimes does Terry have?
18 dimes and 20 quarters
8 dimes and 12 quarters
14 dimes and 16 quarters

Q 4: Eric's wallet has one-dollar bills, five-dollar bills, and ten-dollar bills. The total amount is $43. He has four times as many one-dollar bills as ten-dollar bills. All together, there are 13 bills in his wallet. How many of each bill does he have?
2 ten-dollar bills, 8 one-dollar bills, and 3 five-dollar bills
3 ten-dollar bills, 8 one-dollar bills, and 4 five-dollar bills.
5 ten-dollar bills, 7 one-dollar bills, and 3 five-dollar bills.

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