SOLUTION: Mina had 34 nickels and quarters totaling $4.10. she had two less than twice as many as quarters. how many of each did she have?

Question 218698: Mina had 34 nickels and quarters totaling $4.10. she had two less than twice as many as quarters. how many of each did she have?
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
Since she had 34 coins total, let x = number of one type of coin. It works with either one, but let's just say that x = number of quarters. The rest of the coins, that is 34-x, would be nickels.

Let x= number of quarters
34-x = number of nickels

The equation is based upon the VALUES of each coin TIMES the NUMBER of coins. It can be worked in either DOLLARS or CENTS, but in CENTS, you don't have to use decimals. Remember that $4.10 is actually 410 cents:

25*x + 5*(34-x)= 410
25x + 170 - 5x = 410
20x + 170 = 410
20x = 410-170
20x = 240
x=12 Quarters
34-x=34-12 = 22 Nickels

Check:
12 Quarters = $3.00
22 Nickels = $1.10
Total Value = $4.10. It checks!

For additional explanation on this topic, please go to my website. Do a "Bing" search for my last name "Rapalje". Look for "Rapalje Homepage" at the top of this search. Look near the top of my Homepage for "Basic, Intermediate and College Algebra: One Step at a Time", click on "Basic Algebra" and look in Chapter 1 for the topics near the end of the chapter that are related to Word Problems.

R^2

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
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