A motel clerk counts his $1 and $10 bills at the end of the day. He finds that hes has total of 64 bills having combined monetary value of $217. Find the number of each denomination that he has.
hint: any number that ten goes into has a zero at the end for instance 10x5=50 (which has a zero)
number of tens ---- x
number of ones ---- 64-x
10x + 1(64-x) = 217
9x = 163
x = 17
He had 17 tens and 47 ones
A motel clerk counts his $1 and $10 at the end of a day. He finds that he has a total of 60 bills having a combined monetary value of $168. Find the number of bills of each denomination that he has.
To find the number of each denomination, let's assign variables and set up equations:
Let x be the number of $1 bills.
Let y be the number of $10 bills.
We are given two pieces of information:
1. There are a total of 64 bills: x + y = 64.
2. The combined monetary value is $217: 1x + 10y = 217.
Now, we have a system of two equations with two variables. We can solve it using the substitution method or the elimination method. Let's use the elimination method:
Multiply the first equation by 10 to match the coefficients of y in both equations:
10(x + y) = 10(64)
10x + 10y = 640
Now, subtract the second equation from this modified first equation:
(10x + 10y) - (1x + 10y) = 640 - 217
Simplifying:
9x = 423
Divide both sides by 9:
x = 47
Substitute this value of x back into the first equation to solve for y:
47 + y = 64
y = 64 - 47
y = 17
Therefore, the motel clerk has 47 $1 bills and 17 $10 bills.