Is there other way to solve this question?

<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>

<p>As usual, I tried to do this by playing with numbers. And I sort of backed into an easy answer. Here goes:</p>

<p>First, I looked at 3 and 4 b/c they are in a 3:4 ratio. Then I thought, what would you have to add to each of them to make a 4:5 ratio? That's easy -- add 1 to each. But we are not adding one to each, we are adding 7 to each. So I took my original numbers and multiplied them by 7 (so that the proportional increase would be the same): now I have 21 and 28. And sure enough, if you increase them both by 7 you get 28 and 35 which is still a 4:5 ratio. So increase them by 14 each instead and you get 35 and 42 which are in a 5:6 ratio. So that's the answer.</p>

<p>Then I realized that it was even easier: Notice that the second time, you are increasing them by another 7 each. In other words..</p>

<p>x ----> x+7 ----> x+7+7 = 3 ----> 4 ----> 5</p>

<p>y ----> y+7 ----> y+7+7 = 4 ----> 5 ----> 6</p>

<p>If the formatting of this post doesn't get ruined, you may see what I meant... </p>

<p>Bottom line: if all that algebra you did is the only way to solve the problem then it is NOT a realistic SAT problem.</p>

<p>
[quote]
Then I realized that it was even easier: Notice that the second time, you are increasing them by another 7 each. In other words..</p>

<p>x ----> x+7 ----> x+7+7 = 3 ----> 4 ----> 5</p>

<p>y ----> y+7 ----> y+7+7 = 4 ----> 5 ----> 6

[/quote]
</p>

<p>I hesitated to post a similar answer last night, because "showing" ratio of progression in series is not always straightforward. </p>

<p>This said, it was quite clear that the progression would continue. Once you had</p>

<p>3/4 ----> 4/5 ----> it ought to be 5/6. Fwiw, it will also continue to 6/7 etc. The pattern is is that denominator becomes the next numerator. </p>

<p>:)</p>

<p>Thanks for the answer it made perfect sense,but in the SAT day I sometimes get frustrated about which way to solve it and end up losing some time.</p>