MATH SOLVE

3 months ago

Q:
# lucas divides his pizza into three equal pieces for himself and his two friends. his friend teddy eats 5/8 of his piece for lunch and a further 2/5 of what remains for dinner. what fraction of the original pizza did teddy eat for dinner

Accepted Solution

A:

Answer:He ate [tex]\frac{1}{20}[/tex] of the original pizza for dinnerStep-by-step explanation:- Lucas divides his pizza into three equal pieces for himself and his two friends∵ There are 1 pizza ∵ It is divided into 3 equal parts∴ Each part is [tex]\frac{1}{3}[/tex]∴ Teddy takes [tex]\frac{1}{3}[/tex] of the pizza- Teddy eats [tex]\frac{5}{8}[/tex] of his piece for lunch and a further [tex]\frac{2}{5}[/tex] of what remains for dinner ∵ His piece is [tex]\frac{1}{3}[/tex]∵ He eats [tex]\frac{5}{8}[/tex] of his piece for lunch∴ He eats for lunch = [tex]\frac{5}{8}[/tex] × [tex]\frac{1}{3}[/tex] = [tex]\frac{5}{24}[/tex]- Let us find the remaining of his piece for dinner∵ The remaining = [tex]\frac{1}{3}[/tex] - [tex]\frac{5}{24}[/tex]- Make L.C.M for the denominators∵ The L.C.M of 3 and 24 is 24∵ [tex]\frac{1}{3}[/tex] = [tex]\frac{1*8}{3*8}[/tex] = [tex]\frac{8}{24}[/tex]∴ The remaining = [tex]\frac{8}{24}[/tex] - [tex]\frac{5}{24}[/tex]∴ The remaining = [tex]\frac{3}{24}[/tex] = [tex]\frac{1}{8}[/tex]∵ He ate [tex]\frac{2}{5}[/tex] of the remaining for dinner∵ The remaining of his piece = [tex]\frac{1}{8}[/tex]∴ He ate for dinner ⇒ [tex]\frac{2}{5}[/tex] × [tex]\frac{1}{8}[/tex]∴ He ate for dinner ⇒ [tex]\frac{2}{40}[/tex] = [tex]\frac{1}{20}[/tex]* He ate [tex]\frac{1}{20}[/tex] of the original pizza for dinner