SOLUTION: Mary has $1.45 in nickels and dimes. If she has 4 more dimes than nickels how many of each does she have?

Question 1126901: Mary has $1.45 in nickels and dimes. If she has 4 more dimes than nickels how many of each does she have?
Found 3 solutions by josgarithmetic, Boreal, greenestamps:
Answer by josgarithmetic(39627)   (Show Source): You can put this solution on YOUR website!
n, how many nickels

7 nickels
11 dimes
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
x nickels and x+4 dimes
.05x+(x+4)*.10=1.45
.05x+.10x+.40=1.45
.15x=1.05
x=7 nickels ($0.35)
x+4=11 dimes ($1.10
Answer by greenestamps(13206)   (Show Source): You can put this solution on YOUR website!

Of course you should know how to solve a problem like this using formal algebra, as demonstrated in the response from tutor @boreal.

But this is a good type of problem with which you can get some good mental exercise by solving it informally, using logical reasoning.

And you also can see that the formal algebraic solution does nearly exactly the same thing as the informal solution to get the answer; that helps you see how the formal algebraic solution makes sense.

(1) Imagine the coins on the table in front of you -- nickels and dimes with a total value of $1.45, with 4 more dimes than nickels.

(2) Count the 4 "extra" dimes first. That's 40 cents, leaving $1.05; and now the numbers of nickels and dimes are the same.

(3) One nickel and one dime together make 15 cents; the number of nickels and dimes needed to make the remaining $1.05 (105 cents) is 105/15 = 7.

So there are 7 nickels; the number of dimes is 7 plus the 4 you counted first, for a total of 11.

ANSWER: 7 nickels, 11 dimes.

If you are new to algebra and have trouble seeing why it works, compare this informal solution to the formal one provided by the other tutor; you will see that the calculations are the same in both.
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