Question

A tip jar contains x one-dollar bills and y five- dollar bills. There are 42 bills in the jar, and the total value is $90.00. How many one-dollar bills and how many five-dollar bills are in the tip jar?

Answer 1

Answer:

30 one-dollar bills and 12 five-dollar bills.

Step-by-step explanation:

Let x represent number of one-dollar bills and y represent number of five-dollar bills.

We have been given that a tip jar contains x one-dollar bills and y five- dollar bills. There are 42 bills in the jar. We can represent this information in an equation as:

$x+y=42...(1)$

$x=42-y...(1)$

We are also told that the total value of all bills is $90.00.  We can represent this information in an equation as:

$1x+5y=90...(2)$

Upon substituting equation (1) in equation (2), we will get:

$42-y+5y=90$

$42+4y=90$

$42-42+4y=90-42$

$4y=48$

$\frac{4y}{4}=\frac{48}{4}$

$y=12$

Therefore, there are 12 five-dollar bills in the tip jar.

Upon substituting $y=12$ in equation (1), we will get:

$x=42-y\\\\x= 42-12\\\\x=30$

Therefore, there are 30 one-dollar bills in the tip jar.