<p>The ratio of x to y is 3 : 4, and the ratio of x + 7 to y + 7 is

4 : 5. What is the ratio of x + 14 to y + 14 ?</p>

<p>I solved this using this method -></p>

<p>x/y = 3/4;</p>

<p>(x + 7) / (y + 7) = 4/5;</p>

<p>(x + 7) = 4(y + 7) / 5;</p>

<p>(x + 7) = (4y + 28) / 5;</p>

<p>5(x + 7) = 4y + 28;

5x + 35 = 4y + 28;

5x - 4y = -35 + 28;

5x - 4y = -7;</p>

<p>x/y = 3/4;

x = 3y/4;</p>

<p>5(3y/4) - 4y = -7;</p>

<p>15y/4 - 4y = -7; * 4</p>

<p>4(15y/4 - 4y) = 4 * -7;

15y - 16y = -28;

-y = -28;

y = 28;</p>

<p>x/28 = 3/4;

x = 3(28) / 4;

x = 84 / 4

x = 21;</p>

<p>(21 + 14) / (28 + 14) = 5/6;</p>

<p>So answer is 5/6;</p>

<p>I wanted to know if there is faster way to do this type of questions.</p>