Thread: Ratios and proportions

Hi, i am having a little bit of difficulties with ratios and proportions and would really appreciate if someone could help me understand this problem.

Solve x : 6/8 = 9/x+7

Alright so here's what i would do :

8 * 9 = 72 / 6.

72 divided by 6 = 12

12 + 7 = 19.

x = 19.

Apparently, this is wrong. The correct answer is :

12 - 7 = 5.

x = 5.

My question is, why exactly do you have to subtract 7 instead of adding it?

I don't see why you have the step 12 + 7 = 19. You need to carefully work through the steps for solving for x. First let's use parentheses so it's clear what the problem is:

6/8 = 9/(x+7)

First you can multiply both sides by 8 to get:

8 * 6/8 = 8 * 9/(x +7), or 6 = 72/(x+7)

Note that I use the '*' symbol to mean multiplication, to avoid confusion with the unknown value 'x.'

Now divide both sides by 6:

6/6 = (72/6)/(x +7), or 1 = 12/(x+7)

Now multiply through both sides by (x+7)

(x+7) * 1 = (x+ 7) * 12/(x+ 7), or x+7 = 12

Finally subtract 7 from both sides:

(x+7)-7 = 12 - 7, or x = 5.