Is there other way to solve this question?

GenericMath
Wed, 09 Nov 2011 01:59:04 +0000

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 ?

I solved this using this method ->

x/y = 3/4;

(x + 7) / (y + 7) = 4/5;

(x + 7) = 4(y + 7) / 5;

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

5(x + 7) = 4y + 28;
5x + 35 = 4y + 28;
5x - 4y = -35 + 28;
5x - 4y = -7;

x/y = 3/4;
x = 3y/4;

5(3y/4) - 4y = -7;

15y/4 - 4y = -7; * 4

4(15y/4 - 4y) = 4 * -7;
15y - 16y = -28;
-y = -28;
y = 28;

x/28 = 3/4;
x = 3(28) / 4;
x = 84 / 4
x = 21;

(21 + 14) / (28 + 14) = 5/6;

So answer is 5/6;

I wanted to know if there is faster way to do this type of questions.