Math Problem

Between them, three brothers -Michael, Daniel and Nicholas - eat 2/3 of a pie. If Michael eats 1/4 the amount eaten and Daniel eats 1/5 of what Nicholas eats, what fraction of the pie does Nicholas eat?

Can someone start me off in the right direction. What I have to start is (1/4)(2/3)-(1/5)(1/4)(2/3)-x=0. This is clearly not the correct equation. What am I doing wrong?

m + d + n = 2/3
m = 1/4 d
d = 1/5 n

I know this doesn’t help much, but I get five twelfths doing it in my head. Is that the right answer? :confused:

Between them, Daniel and Nicholas ate three quarters of two thirds of the pie. If Nicholas’ share of this amount was x, then:

x + (x/5) = (3/4) x (2/3)

Nitpick: Your second line should be “m = 1/4 * 2/3”; it says Michael eats “1/4 the amount eaten”, not “1/4 the amount Daniel eats”.

Did it in your head, I am quite jealous.

We have 6x=30/12.

x = 5/12.

You’re right, so it does.

For what it’s worth, ignoring the 2/3 for the moment…

Michael ate 1/4 of the total
That leaves 3/4, which Daniel and Nicholas consumed together.
Daniel ate 1/5 of what Nicholas eats.

n + n/5=3/4
5n/5 + n/5=3/4
n=15/24 or 5/8
So Nichlolas at 5/8 and Daniel ate 1/8

5/8 * 2/3 =10/24, or 5/12=Nicholas’ portion of the total pie

Daniel ate one-fifth of what Nicholas ate, 1/12
Michael ate 1/4 of 2/3, = 2/12.

5/12 + 1/12 + 2/12=8/12, reduces to 2/3 of the overall pie.

Or, to simplify, Daniel and Nicholas ate half the pie. So if Daniel ate 1/5 of what Nicholas ate, Daniel ate 1/6 of the pie and Nicholas ate 5/6. As others have already said.

ETA: Not 1/6 and 5/6, I meant 1/12 and 5/12.

I would solve it this way. Divide the pie into 36 equal pieces. 24 (2/3) were eaten by the three brothers

Michael eats 1/4 of 24 or 6 pieces.

18 pieces are left.

Nichalas eats 5 times as many pieces as Daniel.
Daniel eats 15 pieces and Nicholas eats 3 pcs.

Michael eats 6 out 36 pcs or 1/6 of the pie.
Nicholas eats 15 out 36 pcs or 5/12 of the pie.
Daniel eats 3 out 36 pcs or 1/12 of the pie.

FWIW, Nicholas sounds like my brother. He was a pig too.