# 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?

Mar 1, 2016

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

#### Explanation:

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

Mar 1, 2016

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.

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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 $\left(\text{time")/("saving}\right)$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:

$\text{ "w=9" weeks}$

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