What is the value of 𝑥 if three, 𝑥 plus six, four, and 44 are in proportion?
The first thing we need to do here is set up a proportion. Three over 𝑥 plus six is equal to four over 44. What we want to do now is isolate 𝑥, solve for 𝑥. Because 𝑥 is in the denominator, I want to move it out by multiplying the left side of the equation by 𝑥 plus six over one.
If I multiply the left side by that value, I have to multiply the right side by the same value. 𝑥 plus six over 𝑥 plus six equals one. On the left side of the equation, we now have three; on the right side, four times 𝑥 plus six over 44. We’re still working to isolate our 𝑥-value.
This time, we want to get 44 out of the denominator. So we multiply the right side by 44 over one. And if we do that, we also must multiply the left side by 44 over one. 44 times three equals 132. On the right side, divided by 44 multiplied by 44 cancels out. And we’re left with four times 𝑥 plus six.
To get rid of multiplying by four, we can divide by four on the right and the left four divided by four equals one. Simplified the right side now says 𝑥 plus six. And when we divide 132 by four, we get 33. We subtract six from the right side and the left side: plus six minus six equals zero. 33 minus six equals 27. 27 equals 𝑥 or more commonly 𝑥 equals 27.
This is one way to solve this problem. We solved this problem just with algebra. But I do want to show you another way that you could solve this problem. When I set up the proportion, I noticed that there was a pattern between four and 44.
To go from four to 44, we multiplied by 11. And since we know that we’re dealing with proportions, to get from three to 𝑥 plus six, we would need to multiply three by 11. That means three times 11 must equal 𝑥 plus six. 33 equals 𝑥 plus six.
We found the same equation when we solved with algebra. Then, we subtract six from both sides and end up with 𝑥 equals 27.