Question

If 5 / y = 7 / x = 24 and 12 / y + 2 / x = 24, find the ratio of x to y.

A. 1 / 6
B. 2 / 7
C. 5 / 12
D. 5 / 7

Answer 1

Answer:

• D)  5/7

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Given equations

• 5/y + 7/x = 24
• 12/y + 2/x = 24

Clear fractions

• 5/y + 7/x = 24    ⇒  (5x + 7y)/(xy) = 24    ⇒   5x + 7y = 24xy
• 12/y + 2/x = 24   ⇒  (12x + 2y)/(xy) = 24  ⇒   12x + 2y = 24xy

Compare the two equations, find the x:y ratio

• 5x + 7y = 12x + 2y
• 12x - 5x = 7y - 2y
• 7x = 5y
• x/y = 5/7

Correct choice is D

Answer 2

Answer:

$\textsf{D)} \quad \dfrac{5}{7}$

Step-by-step explanation:

Given equations:

$\begin{cases}\dfrac{5}{y}+\dfrac{7}{x}=24\\\\\dfrac{12}{y}+\dfrac{2}{x}=24\end{cases}$

Rearrange the first equation to eliminate the fractions:

$\dfrac{5}{y}+\dfrac{7}{x}=24$

$\implies \dfrac{5x}{xy}+\dfrac{7y}{xy}=24$

$\implies \dfrac{5x+7y}{xy}=24$

$\implies 5x+7y=24xy$

Rearrange the second equation to eliminate the fractions:

$\dfrac{12}{y}+\dfrac{2}{x}=24$

$\implies \dfrac{12x}{xy}+\dfrac{2y}{xy}=24$

$\implies \dfrac{12x+2y}{xy}=24$

$\implies 12x+2y=24xy$

Substitute the first equation into the second equation:

$\implies 12x+2y=5x+7y$

Rearrange so that x is on the left side and y is on the right side:

$\implies 12x-5x=7y-2y$

$\implies 7x=5y$

Therefore, the ratio of x to y is:

$\implies \dfrac{x}{y}=\dfrac{5}{7}$