# 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?

##### 2 Answers
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."