A motel clerk counts his $1 and $10 bills at the end of a day. He finds that he has a total of 44 bills having a combined monetary value of $161. Find the number of bills of each denomination that he has
x=number of $1 bills
y=number of $10 bills
Solve the following system:
{x+y = 44 | (equation 1)
x+10 y = 161 | (equation 2)
Subtract equation 1 from equation 2:
{x+y = 44 | (equation 1)
0 x+9 y = 117 | (equation 2)
Divide equation 2 by 9:
{x+y = 44 | (equation 1)
0 x+y = 13 | (equation 2)
Subtract equation 2 from equation 1:
{x+0 y = 31 | (equation 1)
0 x+y = 13 | (equation 2)
Collect results:
Answer: |
| {x = 31
y = 13