Question

If $2x + y = 35$ and $3x + 4y = 65$, then find the value of $\frac{x}{y}$.

A) 2

B) 1

C) 3

D) 4

E) None of these

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Answer

The correct answer is C) 3.

We start with the system of equations: $$ 2x + y = 35 \quad \text{(1)} $$ $$ 3x + 4y = 65 \quad \text{(2)} $$

From equation (1), we can express $y$ in terms of $x$: $$ y = 35 - 2x \quad \text{(3)} $$

Substituting equation (3) into equation (2), we obtain: $$ 3x + 4(35 - 2x) = 65 $$ Expanding and simplifying the equation: $$ 3x + 140 - 8x = 65 $$ $$ -5x + 140 = 65 $$ $$ -5x = 65 - 140 $$ $$ -5x = -75 $$ $$ x = \frac{-75}{-5} = 15 $$

Plugging the value of $x$ back into equation (3) to find $y$: $$ y = 35 - 2(15) = 35 - 30 = 5 $$

Finally, calculate $\frac{x}{y}$: $$ \frac{x}{y} = \frac{15}{5} = 3 $$


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