Question

Martina combined different amounts of water, vinegar, and scrubbing alcohol to make 38 milliliter a of a solution for a science experiment. The amount of vinegar was 8 ml less than that of water, and the amount of rubbing alcohol was half the amount of vinegar. This is represented in the equation below:
x+(x-8)+1/2(x-8)=38
What was the difference in the amounts of water and rubbing alcohol Martina combined?

Answer 1

In the equation provided, x = the amount of water in the solution.
First of all, I would multiply both sides by two to get rid of the 1/2 to give 2x + (2x-16) + (x-8) = 76.
Because everything in the equation is addition or subtraction, we can simply ignore the brackets.
Then we can rearrange the equation to give 5x - 24 = 76. You can then add 24 to both sides to give 5x = 100.
Dividing both sides by 5 will give x = 20, therefore Martina put in 20mL of water. We then substitute this value to give the amount of rubbing alcohol which is 1/2(20-8) or 1/2(12) which is 6.
Therefore the difference in the amounts of water and rubbing alcohol is 20 - 6 or 14 milliliters.