1963 TMTA High School Algebra I Contest Problem 29

Problem

A mechanic agreed to work for $12$ days at $$10$ for each day that he worked, forfeiting $$5$ for each day that he was idle. At the end of the $12$ days he received $$75.$ How many days had he worked?

$\text{(A)} \quad 10 \quad \text{(B)} \quad 9 \quad \text{(C)} \quad 5 \quad \text{(D)} \quad 3 \quad \text{(E) NOTA}$

Solution

Suppose the mechanic worked for $x$ days. He earns $10x$ dollars for each day he works and loses $5x$ dollars for each day he is idle, so we can write the equation: $10x + 5(12-x) = 75.$ Solving yields $x = \boxed{\text{(B)} \quad 9}.$

1963 TMTA High School Mathematics Contests (Problems)
Preceded by Problem 28	TMTA High School Mathematics Contest Past Problems/Solutions	Followed by Problem 30

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1963 TMTA High School Algebra I Contest Problem 29

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