SOLUTION: A man has 35 coins consisting of dimes and quarters. The total value is $5.15. How many of each coin does he have? I know that there are 24 dimes and 11 quarters (working it bac

Question 234633: A man has 35 coins consisting of dimes and quarters. The total value is $5.15. How many of each coin does he have? I know that there are 24 dimes and 11 quarters (working it backwards) but I can't figure out what the equation should be to solve for this problem. Can ANYONE please help me?
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A man has 35 coins consisting of dimes and quarters. The total value is $5.15. How many of each coin does he have?
---------------
Quantity Equation: d + q = 35
Value Equation:::10d+ 25q = 5l5 cents
---------------------------------------
Multiply thru the Quantity Equation by 10 to get:
10d + 10q = 350
---
Subtract that from the Value Equation and solve for "q":
15q = 165
q = 11 (# of quarters)
-----
Since d+q = 35, d+11 = 35 ; d = 24 (# of dimes)
==================================================
Cheers,
Stan H.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Let represent the number of dimes. Let represent the number of quarters. Each dime is worth 10 cents, so the value of the dimes, in cents is . Likewise, the value of the quarters is . And the total value of all the coins, in cents, is 515.

Now we can write an equation that describes the number of coins:

And another equation that describes the value of the coins:

Giving you a system of two equations in two variables. Solve for and . Since you have unity coefficients on the first equation, I would use the substitution method to solve this system.

Which leads me to the description of a shortcut method for solving coin and different value ticket problems. Instead of defining a second variable as above, i.e. "Let represent the number of quarters" you can realize up front that there are 35 coins, so if represents the number of dimes, must represent the number of quarters. Then you can just write the single equation for the value thus:

Which is exactly the same place you would be if you solved the first equation for and then substituted into the second equation.

John

RELATED QUESTIONS
mark has 42 coins consisting of dimes and quarters. the total value of his coins is $6.... (answered by lynnlo)
tom has 80 coins consisting of dimes and quarters. if the total value of his coins is... (answered by ewatrrr)
A man has a box of coins that he uses when playing poker with friends. The box currently... (answered by greenestamps)
Travis has a total of 31 coins consisting of nickels and quarters. The total value of the (answered by CubeyThePenguin)
Angelo has 18 coins consisting of nickels and quarters. If the total value of the coins... (answered by richwmiller)
jason has 15 coins in his pocket, consisting of nickels and dimes. the total value of the (answered by JBarnum)
Richard has 22 coins with a total value of $4. If the coins are all quarters and dimes,... (answered by ankor@dixie-net.com)
Ron has 18 coins with a total value of $3.15. The coins are dimes and quarters. How many... (answered by macston)
Jake has 205 coins consisting of nickels, dimes, and quarters. If the total value of the... (answered by drj)