32 - 3/8y = 3/4y + 5

Question

must show work

Answer 1

Hi Donovan,

There are 2 ways I would do this problem, and it's up to people's preferences which one they like more.

1) Getting rid of all fractions.

You may see that the denominations for the fractions you have are 8 and 4, which means if you multiply both sides by 8, then you get rid of all fractions.

8 (32 - ³/₈ y) = 8 (³/₄ y + 5)

simplify

256 - 3y = 6y + 40

Now add 3y to both sides

256 = 9y + 40

Then we subtract 40 from both sides

216 = 9y ___ dividing both sides by y yields

24 = y

2) Working with fractions directly.

First, just add ³/₈ y to both sides which will get rid of y on the left hand side.

32 = ³/₄ y + ³/₈ y + 5

Multiply ³/₄ y by ²/₂ to get the same denominator as ³/₈ y. Note that ²/₂ = 1 so you're just multiplying by 1.

32 = ⁶/₈ y + ³/₈ y + 5

Then apply the rule for adding fractions with the same denominator.

32 = ⁹/₈ y + 5

Subtract both sides by 5.

27 = ⁹/₈y

To get y on its on own the right side, multiply both side by the reciprocal of ⁹/₈, which is ⁸/₉.

27 (⁸/₉) = (⁸/₉) ⁹/₈ y

The coefficient on the right hand side cancels, and the left hand side becomes 27 * 8 / 9 = 24.

24 = y