30 coins, all nickels, dimes, and quarters, worth $4.60. There are three times as many quarters as nickels and two more dimes than quarters.

Question

I have 30 coins, all nickels, dimes, and quarters, worth $4.60. There are three times as many quarters as nickels and two more dimes than quarters. How many of each kind of coin do I have?

*Using three equations in three variables.

I am confused because when I solve for q I get fractions, but fractions wouldn't make sense as an answer to this problem because it has to be whole coins. This is what I have so far:

 

n=amount of nickels           n+d+q=30         n=3q         d=q+2      

d=amount of dimes                 3q+q+2+q=30

q=amount of quarters             5q=28 but when I divide I get the fraction q=28/5

Please help.

Answer 1

If you have 1 nickle, how many quarters do you have? (3)

If you have 4 nickles, you have 3 times as many quarters (3)(4) = 12

If you have n nickles, then you have 3n quarters so 3n = q, you have  a slightly different equation.

 

If you fix this equation and use substitution like you did, you can get the right answer; you can also try to work in the other information that you have - converting all coin values to cents

    5n + 10d + 25q = 460