# 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?

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 $t : \textcolor{w h i t e}{\text{d}} \to \frac{35624 - 31400}{4} = 2112$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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