# Tiago does some work during the school holidays. In one week he spends "x" hours cleaning cars and "y" hours repairing cycles. The tine he spends repairing cycles is at least equal to the time he spends cleaning cars. This can be written as y>x He spends no more than 12 hours working. He spends at least 4 hours cleaning cars. (a) Write down two more inequalities in x an/or y to show this information. [ The drawing part is NEEDED as I dont understand ] (b) Tiago receives \$3 each hour fro cleaning cars and \$1.50 each hour for repairing cycles. (i) What is the least amount he could receive ? (ii) What is the largest amount he could receive ?

1
by hut810

2016-04-11T16:25:02+05:30
Given, "x" is the hours cleaning cars
"y" is the hours repairing cycles.
y
≥x ⇒ (1)
x+y≤12 ⇒(2)
x≥4 ⇒(3)
lets take x=y
substitute in (2)
2x≤12⇔ x≤6
therefore 4≤x≤6 ⇒(4)
as y ≥ x
6≤y≤8 ⇒(5)
Tiago receives \$3 each hour fro cleaning cars and \$1.50 each hour for repairing cycles.
he will earn the maximum amount if he spends the least amount of time in cleaning cars
3x+1.5y≥ 3(4) + 1.5(8) = \$24
he will earn the least  amount if he spends the maximum amount of time in cleaning cars
3x + 1.5y≤ 3(6)+1.5(6) =\$21