a purse containing $3.20 in quarters and dimes has, in all, 20 coins, Find the number of each kind of coin

Question

This is a weighted quantity problem, and I always have trouble with these.

Answer 1

This problem is all about solving for one variable. 

 

Let x=quarters and y=dimes

 

So, x + y = 20

 

Now we use the coins value and total amount of money to write an equation. (Ive removed decimals for visual ease)  25x + 10y = 320

 

Let's rewrite the original equation in terms of y.... y = 20 - x

 

Now, we will plug this in to the second equation in place of y.... 25x + 10(20-x) = 320

 

Solve for x....25x + 200 - 10x =320. 

 

15x = 120

 

x = 8 quaters

 

Therefore, y = 20 - 8 = 12 dimes