A motel clerk counts his $1 and $10 bills at the end of a day. He finds that he has a total of 70 bills having a combined monetary value of $250. Find the number of bills of each denomination that he has.
x = $1 bills
y = $10 bills
He finds that he has a total of 70 bills means:
x + y = 70
A combined monetary value of $250 means:
x ∙$1 + y ∙ $10 = $250
Now you must solve system:
x + y = 70
x + 10 y = 250
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In first equation subtract y to both sides
x = 70 - y
In second equation replace x with 70 - y
70 - y + 10 y = 250
70 + 9 y = 250
Subtract 70 to both sides
9 y = 180
y = 180 / 9
y = 20
x = 70 - y = 70 - 20
x = 50
50 $1 bills
20 $10 bills
Check result:
x + y = 20 + 50 = 70
50 ∙ $1 + 20 ∙ $10 = $50 + $200 = $250