Algebra 2 word problems

Question

A student has some​ $1 and​ $5 bills in his wallet. He has a total of

16 bills that are worth ​$44. How many of each type of bill does he​ have?

Answer 1

This is a problem that is going to require using a system of equations to solve. A system needs the same amount of equations as variables. To elaborate, if you have 1 variable in one equation then you can solve for it, but if you have 2 variables then you will need 2 equations to solve for both of them.

You have 2 variable because you are "How many of each bill does he have?" That means, how many $1 's and how many $5's.

Call the amount of $1's x and the amount of $5's y.

Since he has 16 bills in all: x + y = 16

Since all the $1's plus all the $5's amount to $44: 1x + 5y = 44

Solve this system for x and y using substitution or elimination.

Answer 2

Considering that the Student has only 1$ and 5$ bills below are all possible ways ot have $44.

1. 4 bills of $1 and 8 bills of $5
2. 9 bills of $1 and 7 bills of $5
3. 14 bills of $1 and 6 bills of $5

Same can be presented with below set of equations where x = number of $5 bills and y = number of $1 bills

x + y = 16

5x + y = 44

That provides an answer for x = 9 bills of $1 and y = 7 bills of $5