Question

A cash box of $1 and $5 bills is worth $45. The number of $1 bills is three more than the number of $5 bills. How many of each bill does it contain?

PLEASE HELP ME!!!!!!!!!!!

Answer 1

• 7 $5 bills
• 10 $1 bills

Explanation:

If we take out the extra $3, we can group the bills into one each of $5 and $1, for a value of $6. There will be 7 such groups in the remaining $42.

That means there are 7 bills of the $5 denomination, and 3 more than that (10 bills) of the $1 denomination.

There are 7 $5 bills and 10 $1 bills.

_____

If you want to write an equation, it is usually best to let a variable stand for the most-valuable contributor. Here, we can let x represent then number of $5 bills. Then the value of the cash box is ...

5x +(x+3) = 45

6x = 42 . . . . . . . . subtract 3, collect terms

x = 7 . . . . . . . . . . . there are 7 $5 bills

x+3 = 10 . . . . . . . . there are 10 $1 bills

You may notice that this working parallels the verbal description above. (After we subtract $3, x is the number of $6 groups.)