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?

1 Answer
Tony B
Jul 29, 2018

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#

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