What percent of 7y is 119?

1 Answer
Feb 27, 2018

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)