SOLUTION: You have 25 coins consisting of dimes and quarters. You have a total of $5.95. How many dimes and how many quarters do you have? Solve using a system of equations. It would be g

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Question 1066327: You have 25 coins consisting of dimes and quarters. You have a total of $5.95. How many dimes and how many quarters do you have? Solve using a system of equations.
It would be great if you could answer this for me thank you!
Found 2 solutions by addingup, ikleyn:
Answer by addingup(3677)   (Show Source): You can put this solution on YOUR website!
Using the substitution method:
d+q = 25 subtract d from both sides:
q = 25-d
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0.10d+0.25q = 5.95 substitute for q:
0.10d+0.25(25-d) = 5.95
0.10d-0.25d+6.25 = 5.95
-0.15d = -0.30 divide both sides by -0.15 and remember -/- = +
d = 2 You have 2 dimes
q = 25-d = 25-2 = 23
------------------------------
check:
0.25(23) = 5.75
0.10(2) = 0.20
Total . . .5.95 Correct
Answer by ikleyn(53763)   (Show Source): You can put this solution on YOUR website!
.
A lot of money !!

Probably, all coins are quarters ! - Let's check.

25 quarters are worth 25*25 = 625 cents.

Exactly 30 cents more than the given 595 cents.

Why the given is 30 cents less than 625 cents ??

Because some of 25 quarters must be replaced by real dimes.

How many? The difference between a quarter and a dime is 15 cents. 


Hence WHAT ?? - Exactly two of 25 quarters must be replaced by dimes.


Answer. 2 dimes and 23 quarters.

Check. 2*10 + 23*25 = 595 cents.


So, I showed you how to solve this simple problem MENTALLY, WITHOUT using equations.
But you can solve it with equations, too.
Exactly as the other tutor did it for you.

You may ask me: for what reason did I show it to you ?

The answer is: to take you out of the box.

--------------------
There is entire bunch of lessons on coin problems
    - Coin problems
    - More Coin problems
    - Solving coin problems without using equations
    - Kevin and Randy Muise have a jar containing coins
    - Typical coin problems from the archive
    - More complicated coin problems
    - Solving coin problems mentally by grouping without using equations
    - Santa Claus helps solving coin problem
    - OVERVIEW of lessons on coin word problems
in this site.

Read them and become an expert in solution of coin problems.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Coin problems".


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