2/3 of the coins in a collection of quarters and dimes are quarters. The collection is worth $12. How many dimes are there?

quarters-and-dimes

#1

2/3 of the coins in a collection of quarters and dimes are quarters. The collection is worth $12. How many dimes are there?

Answer:

I’m assuming your topic is system of equations
Set your variables first, let x be quarter and y be dime
now, you know how much they are all worth, and the value of each coin relative to each other so you can write .25x+.1y=12
These numbers were found because you know that a quarter is 25 cents, which is .25 of a dollar and a time is .1 dollar and both add up to 12 dollars.
Now your second equation is much simpler, you know that 2/3 of the coins are quarters. This means that you have two quarters for every dime so x=2y
.25(2y)+.1y=12
.6y=12
y=20
20 dimes