Question

Given that `5(19/15)+5y=9` what is the value of `y`?

Answer 1

`y=8/15`

Explanation:

`color(blue)("Approach 1")`

`5(19/15)` is the same as `5xx19/15`

It is also the same as: `5/15xx19" "->" "(cancel(5)^1)/(cancel(15)^3)xx19`

Write as: `19/3+5y=9`

subtract `19/3` from both sides

`5y=9-19/3`

but 9 is the same as `27/3`

`5y=(27-19)/3 = 8/3`

Divide both sides by 5

`y=8/(3xx5)=8/15`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Approach 2")`

`5(19/15)+5y=9`

Factor out the 5

`5(19/15+y)=9`

divide both sides by 5

`19/15+y=9/5`

Subtract `19/15` from both sides

`y=9/5-19/15`

`y=27/15-19/15=8/15`