Question

How do you solve `\frac{y}{6} + \frac{y}{3} = \frac{5}{8}`?

Answer 1

See a solution process below:

Explanation:

First, multiply the `y/3` term by the appropriate form of `1` to create a common denominator with the other `y` fraction and the add the fractions:

`y/6 + (2/2 xx y/3) = 5/8`

`y/6 + (2 xx y)/(2 xx 3) = 5/8`

`y/6 + (2y)/6 = 5/8`

`(y + 2y)/6 = 5/8`

`(1y + 2y)/6 = 5/8`

`((1 + 2)y)/6 = 5/8`

`(3y)/6 = 5/8`

`(3y)/(3 xx 2) = 5/8`

`(color(red)(cancel(color(black)(3)))y)/(color(red)(cancel(color(black)(3))) xx 2) = 5/8`

`y/2 = 5/8`

Now, multiply each side of the equation by `color(red)(2)` to solve for `y` while keeping the equation balanced:

`color(red)(2) xx y/2 = color(red)(2) xx 5/8`

`cancel(color(red)(2)) xx y/color(red)(cancel(color(black)(2))) = color(red)(2) xx 5/((2 xx 4))`

`y = cancel(color(red)(2)) xx 5/((color(red)(cancel(color(black)(2))) xx 4))`

`y = 5/4`

Or

`y = 1.25`