A Problem In My Hostel.

Algebra Level 3

Mus and Syukri had had a meal together to which Mus contributed 5 loaves and Syukri contributed 3 loaves of bread. A third person, Adli, joined them, but didn't bring any loaves of bread. The three of them shared their meal, and ate equal portions of bread.After the meal Adli placed down 8 dollars and left. When Mus and Syukri wanted to divide the money between them, they quarrelled.

Muss said: "I should get 5 dollars and you Syukri , should get only 3 dollars , This is a fair distribution, based on the ratio the loaves that each of us had contributed."

Syukri refused and insisted that "But we ate equal portions of bread, so there should be an equal division of the money. Each of us should get 4 dollars."

So, to solve the problem, they seek help from their brilliant friend Faiz Aiman. What was Faiz Aiman's reply?

Both of them will get 4 dollar each Mus will get 5 dollar while Syukri will get 3 dollar Mus will get 6 dollar while Syukri will get 2 dollar Mus will get 7 dollar while Syukri will get 1 dollar.

2 solutions

Uahbid Dey
Apr 8, 2014

M ate 8/3 of the total. He contributed 5. Hence he is actually giving away 5-(8/3) i.e. 7/3 portion. Similarly S giving away 3-(8/3) i.e. 1/3 portion. This (7/3)+(1/3) = 8/3 portion was eaten by A. So ratio is (7/3):(1/3) i.e. 7:1

Here's an easier way to think about it. "A" ate 8/3 loves, and paid $8. This means that each bread is worth $3 ($8 / (8/3)). In monetary scale, M contributed $15 (=5 * $3) upfront, and S contributed $9 (=3 * $3) upfront. They each had $8 worth of bread (=8/3 * $3), so M can take back $7 (=$15 - $8), and S can take back $1 (=$9 - $1).

Sung Cho - 7 years, 2 months ago

same way :D

Jeremi Ferdian - 7 years, 2 months ago

Very Nice Way.

Abhu Jadhav - 7 years, 1 month ago

Somesh Singh
Apr 11, 2014

as adli gave 8$ therefore the per person cost was 8$. which means that the total cost of the three persons= cost of 8 loaves =cost per person X 3=24$.
now, cost of 8 loaves=24$
hence, 1 loaf cost= 3$.
hence mus's contri.=5X3=15$ and syu's contri=3X3=9$

now to determine how much each one should get, subtract the cost of loaf that each one ate

for mus=15$-8$=7$ and for syu=9$-8$=1$

no need much explanation, keep t short hahaha. Adli didn't contribute anything so he is "suppose" to get less money

Abraham Pestana - 7 years ago

A Problem In My Hostel.

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