Question

Jose is saving to purchase a bike. He can set aside $12 per week from his earrings. He already has $35 set aside for purchasing a bike. How many weeks will it take him to save enough to purchase a bike for $225?

Answer 1

As you can only have complete weekly units it will take 16 weeks.
He will have a bit of extra cash saved

Explanation:

Total cost `" "->$225`
Saved so far `->$color(white)(2)35`

Extra to save`-> $225`
`" "ul(color(white)($2)35) larr" Subtract"`
`" "$190`

Let the count of weeks be `w`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Using shortcut method")`

`$12xxw=$190`

Divide both sides by $12

`color(red)(w=($190)/($12)) -> 190/12= 15.833` weeks to 3 decimal places

As you can only have weekly units it will take 16 weeks.
He will have a bit of extra cash saved

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Using ratio (shortcut method derived from this approach)")`

`("weeks")/("savings") = 1/($12) -=w/($190)`

We need to change the $12 into $190. As this is a ration we must maintain proportionality so what we do to the bottom we also do to the top (for multiply and divide).

`("weeks")/("savings") = 1/($12)`

Divide top and bottom by 12

`=(1-:12)/(12-:12) =(1-:12)/1`

Multiply top and bottom by 190

`(color(green)(1-:12xx190))/(1xx190)= 15.833/190=w/($190)`

`w=15.833` weeks to 3 decimal places
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Footnote")`

Notice that `color(green)(1-:12xx190)` is the same as

`color(red)(color(green)(1/12xx190) = 190/12 = w)" "` as in the shortcut