Please solve in algebra format

Question

Two thirds of the coins in a collection of quarters and dimes are quarters. The collection is worth $12. How many dimes are there?

Answer 1

That means the other third is dimes--so you have twice as many quarters as dimes.

 

Set up 2 equations:

 

q = 2d, "the number of quarters is twice the number of dimes."

 

and

 

25q + 10d = 1200, "25 cents times the number of quarters, plus 10 cents times the number of dimes, equals 1200 cents, or 12 dollars."

 

Now, since you know that q = 2d, every time you see a q, replace it with 2d:

 

25(2d) + 10d = 1200, so

 

50d + 10d = 1200, so

 

60d = 1200. now divide both sides by 60, which gives you

 

d = 20. Which means you have 20 dimes. And since you have twice as many quarters, that means you have 40 quarters.

 

Check:

 

20 dimes = 20 x 10 cents = 200 cents (or 2 dollars)

40 quarters = 40 x 25 cents = 1000 cents (or 10 dollars)

 

2 dollars + 10 dollars = 12 dollars. WOO HOO!

 

Remember that the specific question is "how any dimes are there," so your answer should be "there are 20 dimes in the collection, Mrs. TeacherFace..."

 

:-)  hope this helps!

 

Matt