Question

The maximum Youth Allowance is reduced by $1 for every $4 that the youth's parents income is over $31 400. By how much is Hannah's Youth Allowance reduced if her parents earn a combined income of $35 624?

Answer 1

Hannah's reduction in Youth Allowance is `$2112`

Explanation:

Let the total income be `t`

Then the amount over `$31400" "` is `" "$[t-31400]`

The count of every every $4 in `$[t-31400] -> ($[t-31400])/($4)`

Notice the way in which the units of measurement ($) cancels out leaving just a count: `color(white)("d")-> color(white)("d") (cancel($)[t-31400])/(cancel($)4)`

We are told that the actual joint income is $35624.00

This is substituted for `t: color(white)("d")-> (35624-31400)/4 = 2112`

For each of these counts the youth allowance is reduced by $1

Total reduction in Hannah's allowance is: `$1 xx 2112 = $2112`