Question

Harry, Mark, Zane and Tom bought a refrigerator for their aunt. Harry paid 1/3 of what the rest paid. Mark paid 1/4 of what the rest paid. Zane paid 1/6 of what the rest paid. Tom paid $176 more than Harry. How much did the refrigerator cost?

Answer 1

If someone paid 1/h of what the rest paid, then 4 of the next paid T, then he paid T/h, so the total cost was
T + T/h = T(1 + 1/h) = T/h(h + 1), it means that he paid the total cost’s 1/(h + 1) part since T/h(h + 1)/(h + 1) = T/h.
Suppose that the cost of refrigerator was x, then
Harry paid 1/3 of what the rest paid, so he paid x/4,
Similarly Mark paid x/5, Zane paid x/7.
Tom paid 176 dollars more than Harry, so paid x/4 + 176.
Since they paid x, it gives that:
x/4 + x/5 + x/7 + (x/4 + 176) = x
35x + 28x + 20x + 35x + 24640 = 140x
118x + 24640 = 140x
24640 = 22x
1120x
The required solution is 1120 dollars