Money Word Problems

The value of a collection of coins or bills each of which has the same value is obtained by multiplying the number of coins or bills by the value of one coin or bill.

The value of a nickel is $0.05. The value of 4 nickels is 4 times $0.05, which is $0.20.

The value of a ten-dollar bill is $10. The value of 7 ten-dollar bills is 7 times $10, which is $70.

Bill has 8 coins. Each coin is either a nickel or a dime. The value of all 8 coins is $0.65.

How many of the 8 coins are nickels? How many of the 8 coins are dimes?

Let x be the number of nickels. Then the number of dimes is $8 - x$ .

Name of Coin	Value of One Coin (dollars)	Number of Coins	Value of Coins (dollars)
nickel	0.05	`x`	$0.05 x$
dime	0.10	$8 - x$	$0.10 (8 - x)$

The equation states that the value of the nickels plus the value of the dimes is $0.65.

$0.05 x + 0.10 (8 - x) = 0.65$

Multiply each side by 100.

$5 x + 10 (8 - x) = 65$

$5 x + 80 - 10 x = 65$

$- 5 x + 80 = 65$

$- 5 x + 80 - 80 = 65 - 80$

$- 5 x = - 15$

$\frac{- 5 x}{- 5} = \frac{- 15}{- 5}$

$x = 3$

x, which is 3, is the number of nickels. The number of dimes is $8 - x$ , which is $8 - 3$ or 5.

There are 3 nickels and 5 dimes.

A cash box contains 20-dollar bills and 10-dollar bills only. They are worth a total of $510. There are 3 more 10-dollar bills than 20-dollar bills.

How many 20-dollar bills are in the cash box? How many 10-dollar bills are in the cash box?

Let x be the number of 20-dollar bills. Then the number of 10-dollar bills is $x + 3$ .

Name of Bill	Value of One Bill (dollars)	Number of Bills	Value of Bills (dollars)
20-dollar bill	20	`x`	$20 x$
10-dollar bill	10	$x + 3$	$10 (x + 3)$

The equation states that the value of the 20-dollar bills plus the value of the 10-dollar bills is $510.

$20 x + 10 (x + 3) = 510$

$20 x + 10 x + 30 = 510$

$30 x + 30 = 510$

$30 x + 30 - 30 = 510 - 30$

$30 x = 480$

$\frac{30 x}{30} = \frac{480}{30}$

$x = 16$

x, which is 16, is the number of 20-dollar bills. The number of 10-dollar bills is $x + 3$ , which is $16 + 3$ or 19.

There are 16 20-dollar bills and 19 10-dollar bills.

A theater has two ticket prices. An adult ticket costs $12, and a child ticket costs $5. The theater sold 100 tickets to a Saturday show for $626.

How many adult tickets did the theater sell? How many child tickets did the theater sell?

Let x be the number of adult tickets. Then the number of child tickets is $100 - x$ .

Type of Ticket	Ticket Price (dollars)	Number of Tickets	Value of Tickets (dollars)
adult	12	`x`	$12 x$
child	5	$100 - x$	$5 (100 - x)$

The equation states that the value of the adult tickets plus the value of the child tickets is $626.

$12 x + 5 (100 - x) = 626$

$12 x + 500 - 5 x = 626$

$7 x + 500 = 626$

$7 x + 500 - 500 = 626 - 500$

$7 x = 126$

$\frac{7 x}{7} = \frac{126}{7}$

$x = 18$

x, which is 18, is the number of adult tickets. The number of child tickets is $100 - x$ , which is $100 - 18$ or 82.

The theater sold 18 adult tickets and 82 child tickets.