Question

Anna is saving $6.35 a week to buy a computer game that costs $57.15. How many weeks will she have to save to buy the game?

Answer 1

Divide the total amount by the amount saved per week to find the number of weeks.

Explanation:

`($57.15)/($6.35)=9` weeks.

Answer 2

9 weeks.

I have demonstrated where the shortcut method comes from!

Explanation:

There are shortcut methods that are used so much that they tend to be taken for granted. These shortcuts are based on first principle approaches but help you to skip a lot of stages.

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
To help understanding of what is going on with this I am going to use the first principles method.

We are given an initial condition of $6.35 saved in a week.

This can be expressed as `("time")/("saving")` and viewed as ratio rather than as a fraction.

The ratio is fixed so we can equate initial condition directly to target condition.

Let the length of time to save the full amount in weeks be `w`

`" "color(blue)(("time")/("saving") = 1/($6.35)=w/($57.15))`

The objective is to get `w` on its own on one side of the equals sign and everything else on the other side.

`color(brown)("Multiply both sides by "$57.15)`

`" "color(blue)(1/($6.35)color(brown)(xx$57.15)=w/($57.15)color(brown)(xx$57.15))`

`" "color(blue)((1xxcolor(brown)($57.15))/($6.35)=wxx(color(brown)($57.15))/($57.15))`

But `($57.15)/($57.15)=1`

`" "($57.15)/($6.35) = w`

Dividing out gives:

`" "w=9" weeks"`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(green)("Now you see where the "(57.15)/(6.35) color(white)(.)"comes from."`