1963 TMTA High School Algebra I Contest Problem 36

Problem

Find the fraction which equals 1/4 when 3 is subtracted from the numerator, but equals 1/2 when 2 is added to the denominator.

$\text{(A)} \quad 3/4 \quad \text{(B)} \quad 8/5 \quad \text{(C)} \quad 2/3 \quad \text{(D)} \quad 5/8 \quad \text{(E) NOTA}$

Solution

Let the original fraction be $\frac{x}{y}.$ We can write the system of equations" $\frac{x-3}{y}=\frac{1}{4}$ $\frac{x}{y+2}=\frac{1}{2}$ Solving, we get $\frac{x}{y}=\boxed{\text{(D)} \quad 5/8}.$

1963 TMTA High School Mathematics Contests (Problems)
Preceded by Problem 35	TMTA High School Mathematics Contest Past Problems/Solutions	Followed by Problem 37

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1963 TMTA High School Algebra I Contest Problem 36

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