Question

What percent of 7y is 119?

Answer 1

A bit of teaching about percentages given as you used that word.

Suppose you mean: given that `7y=119` what is `y`
The answer to this is `y=17`

Explanation:

`color(blue)("Teaching about percentage")`

Let me demonstrate by example:

Have a bag of sweets that contains a total of 50 sweets.

From that 50 we select 3 sweets. Then as a fraction of the whole we have `3/50` of the whole bag of sweets.

Percentage is just a fraction but a special one. What makes it special is that the bottom number is always 100.

So percentage in fraction format is `("some count")/100`

Lets convert our `3/50` into percentage.

We need to make the bottom number become 100.

If you multiply by 1 you do not change the value. However, 1 comes in many forms.

`color(green)(3/50color(red)(xx1) color(white)("dddd") =color(white)("dddd")3/50color(red)(xx2/2))`

`color(green)(color(white)("ddddddddd")->color(white)("ddddd")(3xx2)/(50xx2))`

`color(green)(color(white)("ddddddddd")->color(white)("dddddd")6/100)`

We now have our percentage as a fraction.

`color(green)("Another way of writing this is "6%)`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Determine the value of "y" from "7y=119)`

`color(purple)("Using first principles to explain what is happening")`

`color(purple)("Shortcut methods are just remembering what happens")` `color(purple)("in first principles")`

This is the same as `7xxy=119`

We need to get `y` on its own on one side of the = and everything else on the other side.

We can turn the 7 into 1. Divide both sides of the = by `color(red)(7)`

`color(green)(7y=119 color(white)("dddd")->color(white)("dddd")7/color(red)(7)y=119/color(red)(7))`

But `7/7` is the same as 1

`color(green)(color(white)("ddddddddddd")->color(white)("dddd")1xxy=17`

`color(green)(color(white)("ddddddddddd")->color(white)("dddd")y=17)`