SOLUTION: Elaine has 88 coins in a purse which are all 5-cent coins and 10-cent coins. The total value of the coins are $7. How many of each type of coin does she have

Question 1035084: Elaine has 88 coins in a purse which are all 5-cent coins and 10-cent coins. The total value of the coins are $7. How many of each type of coin does she have

Found 2 solutions by ikleyn, Theo:
Answer by ikleyn(52858) (Show Source): You can put this solution on YOUR website!
.
Elaine has 88 coins in a purse which are all 5-cent coins and 10-cent coins. The total value of the coins are $7.
How many of each type of coin does she have?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Let n be the number of nickels (5-cent coins) Elain has. Then the number of dimes (10-cent coins) is (88-n). n nickels contribute 5n cents into the total. (88-n) dimes contribute 10*(88-n) cents into the total. So, you have this "value" equation 5n + 10*(88-n) = 700 cents. Simplify and solve: 5n + 880 - 10n = 700, or -5n = 700 - 880, -5n = -180, n = = = 36. So, Elaine has 36 nickels (5-sent coins) and 88-36 = 52 dimes (10-cent coins). Check. 5*36 + 10*52 = 180 + 520 = 700 cents. Correct!

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
x = number of 10 cent coins.
y = number of 5 cent coins.
10 * x = total number of cents in x number of 10 cent coins.
5 * y = total number of cents in y number of 5 cent coins.
since you are dealing in cents, then you need to convert everything to cents.
dollars * 100 = cents.
7 dollars is equal to 700 cents.

total number of coins is 88, so you get x + y = 88.

total value in cents is equal to 700, so you get 10x + 5y = 700.

you have 2 equations that need to be satisfied simultaneously.

they are:

x + y = 88
10x + 5y = 700

if you multiply both sides of the first equation by 10 and leave the second equation as is, you get:

10x + 10y = 880
10x + 5y 700

if you subtract the second equation from the first, you get:

5y = 180.

divide both sides of this equation by 5 to get:

y = 36.

since x + y = 88, then x = 88 - 36 = 52.

since x = 52 and y = 36, you get:

10x + 5y = 10*52 + 5*36 = 520 + 180 = 700.

the solution looks good.
you have 52 ten cent coins and you have 36 five cent coins.
their sum is 700 cents which is equal to 7 dollars.

RELATED QUESTIONS
Ryan has 10-cent coins, 20-cent coins and 50-cent coins in his coin bank. 46 of them are... (answered by ankor@dixie-net.com)
There are eight times as many 10 cent coins as there are 5 cent coins in a money box. (answered by josmiceli)
A purse containing only $5 and $10 coins,has 6 more $10 coins than $5 coins. The total... (answered by josgarithmetic)
In my purse I have 21 coins, all of which are either 5-cent or 20-cent coins. Their total (answered by ikleyn)
I have a purse with several coins in it. The coins have values of 1 cent, 5 cents, 10... (answered by ankor@dixie-net.com)
A money box contains only 20 cent coins and 50 cent coins. If there are 57 coins in the... (answered by stanbon)
i have 36 coins all of which are 5 cent or 10 cent if the total value is 3.20 how many... (answered by fractalier)
A purse, containing only 5 peso and 10 peso coins, has more 10 peso coins than 5 peso... (answered by Fombitz)
A coin purse contains 5 cents, 10 cents and 25 cents coins. The number of 10 cents-coins... (answered by ikleyn)