Question

A motel clerk counts his $1 and $10 bills at the end of the day. He finds that he has a total of 52 bills having a combined monetary value of $187. Find the number of bills of each denomination that he has. The clerk has ones and tens.

a) 13 ones, 39 tens
b) 17 ones, 35 tens
c) 21 ones, 31 tens
d) 26 ones, 26 tens

Answer 1

By solving the system of linear equations derived from the total number of bills and their combined value, we can determine that the clerk has 37 $1 bills and 15 $10 bills.

Step-by-step explanation:

The question requires us to solve a system of linear equations where we need to find the number of $1 bills and $10 bills. Let's assume the number of $1 bills is x and the number of $10 bills is y. We have two equations from the given information: x + y = 52 (the total number of bills) and 1x + 10y = 187 (the total monetary value of the bills).

• Equation 1: x + y = 52
• Equation 2: 1x + 10y = 187

We can solve these equations simultaneously. Start by solving the first equation for x: x = 52 - y. Then substitute this expression for x in the second equation, giving us 52 - y + 10y = 187. Simplifying this, we get 9y = 135, and solving for y we find y = 15. Substituting back into the first equation, we get x = 52 - 15 = 37.

Therefore, the clerk has 37 $1 bills and 15 $10 bills.