Word problems involving inequalities

Question

Four children earn money for a charity. Dauda earns #y, Obi earns half as much as Dauda, Chidi earns three times as much as Obi, and wale earns #250 less than all the other three. Together, they earn more than #4300. Find the least value of y.

Answer 1

Hi Aduragbemi,

So the question is a little bit ambiguous for one small reason:

wale earns #250 less than all the other three

It is not clear whether this means 250 less than the minimum of the other three or 250 less than the other three combined. I will answer the question in the case that it means the other three combined (which I expect is what was intended).

I will use variables d,o,c,w to keep track of the amounts earned by Dada, Obi, Chidi, Wale. We have

d = y

o = y/2

c = 3y/2

w = y + y/2 + 3y/2 - 250

Together, they earn y+y/2+3y/2+y+y/2+3y/2-250 = 6y - 250.

If we must have this amount be at least 4300, then we have

6y - 250 ≥ 4300

so this means

6y ≥ 4050

and therefore

y ≥ 4050/6 = 675. Therefore the minimum value is y = 675.

I hope that helps!