Gin has 72$. Word problems in algebra.

Question

Gin has 72$. Has 1$, 5$, and 20$ bills. Gin has three times as many ones as fives and half as many twenties as fives. I want to check my answer. I have to have an algebraic expression and answer it. 

Answer 1

This is a classic linear system, where you have three variables to solve for: 1) how many $1 bills, 2) how many $5 bills, and 3) how many $20 bills. Whatever number of variables you need to solve for, that's the same number of equations you'll need.

 

So without giving too much away, how can we express that all three of our variables (x, y, and z) must add up to $72?

 

How do we express that x, our number of $1 bills, is three times y, the number of $5 bills we have?

 

How do we express that z, the number of $20 bills, is half of y, the number of $5 bills we have?

 

Remember you need three equations to solve for three variables. Once you have the equations, you can solve the system by substitution or elimination. Hope that's a good hint.