Fractional Word problems

Question

Lucas divides a pizza into 3 equal slices for him and his two friends. His friend eats 5/8 of his piece for lunch and a further 2/5 of what remained for dinner. What Fraction of the original pizza did his friend eat for dinner? I think that the answer is 1/20 But the edexcel igcse textbook answer says it is 1/12 can anyone explain me which answer is correct pls?

Answer 1

You are correct and the text book is incorrect

Altogether, of his slice he ate 5/8+2/5 = 25/40 + 16/40 = 41/40 > 1,

which is not allowed.

The answer in the text comes from 1/3*5/8*2/5 = 10/120 = 1/12,

which is 2/5 of what he eat for lunch

But the way the question is worded, it sound like this:

for lunch: 1/3 * 5/8 = 5/24

the misleading part is "2/5 of what remained"

after lunch, 1/3 * (1 - 5/8) = 1/3*3/8 = 3/24 = 1/8 remains

he ate 2/5 of that for dinner, which is 2/5*1/8 = 2/40 = 1/20 <-- your answer is correct

so altogether he ate 5/24 + 1/20 = 25/120 + 6/120 = 31/120

note that 5/8 + 1/20 = 100/160 + 8/160 = 108/160 = 54/80 = 27/40 < 1

very confusing