SOLUTION: Sarah has $5.25 worth of change in nickels and dimes. If she has 3 times as many nickels as dimes, how many of each type of coin does she have?

Question 1203578: Sarah has $5.25
worth of change in nickels and dimes. If she has 3
times as many nickels as dimes, how many of each type of coin does she have?
Found 4 solutions by MathLover1, ikleyn, josgarithmetic, greenestamps:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

nickels:
dimes:
=$
=$
Sarah has $
...eq.1
If she has times as many nickels as dimes, we have
.....eq.2
...solve for

.....both sides multiply by

go to eq.2, substitute the number of dime

Sarah have nickels and dimes.
check:
which verifies our solution

Answer by ikleyn(52891)   (Show Source): You can put this solution on YOUR website!
.

According to the problem, the coins can be grouped in sets, containing 3 nickels and one dime in each set. Thus each set is worth 3*5 + 10 = 25 cents, and the number of sets is = 21. It gives the ANSWER: there are 21 dimes and 3*21 = 63 nickels. CHECK. 21*10 + 63*5 = 526 cents, in total, or $5.25. ! correct !

Solved (mentally).

Answer by josgarithmetic(39630)   (Show Source): You can put this solution on YOUR website!
d dimes
n nickels

Money quantity $5.25.
----------here equation in a single variable

--
Answer by greenestamps(13209)   (Show Source): You can put this solution on YOUR website!

Being able to solve the problem using formal algebra, as a couple of the other tutors did in their responses, is an important mathematics skill. And perhaps that is what you were expected to do.

But doing that mostly gives you practice in following well-defined processes; it doesn't do much to improve your skill at problem solving.

For good problem-solving practice and excellent mental exercise, solve the problem mentally, as tutor @ikleyn did.

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