Let Sarah have "M" number of sweets and Henry have "N" number of sweets.
• Sarah and Henry share some sweets in the ratio 5:6.
According to question,
\Rightarrow\:\dfrac{M}{N}\:=\:\dfrac{5}{6}⇒
N
M
=
6
5
______ (eq 1)
\Rightarrow\:M\:=\:\dfrac{5N}{6}⇒M=
6
5N
_____ (eq 2)
• Sarah eats 24 of her sweets and the ratio of sweets left becomes 1:2.
According to question,
\Rightarrow\:\dfrac{M\:-\:16}{N}\:=\:\dfrac{1}{2}⇒
N
M−16
=
2
1
Cross multiply them
\Rightarrow\:2(M\:-\:16)\:=\:1(N)⇒2(M−16)=1(N)
\Rightarrow\:2M\:-\:30\:=\:N⇒2M−30=N
\Rightarrow\:2 \bigg(\dfrac{5M}{6} \bigg)\:-\:30\:=\:N⇒2(
6
5M
)−30=N
\Rightarrow\:\dfrac{5M}{3}\:-\:30\:=\:N⇒
3
5M
−30=N
\Rightarrow\:\dfrac{5M\:-\:90}{3}\:=\:N⇒
3
5M−90
=N
\Rightarrow\:5M\:-\:90\:=\:3N⇒5M−90=3N
\Rightarrow\:5M\:-\:3M\:=\:90⇒5M−3M=90
\Rightarrow\:2M\:=\:90⇒2M=90
\Rightarrow\:M\:=\:45⇒M=45
Put value of M in (eq 2)
\Rightarrow\:45\:=\:\dfrac{5N}{6}⇒45=
6
5N
Cross multiply them
\Rightarrow\:45(6)\:=\:5N⇒45(6)=5N
\Rightarrow\:270\:=\:5N⇒270=5N
\Rightarrow\:N\:=\:54⇒N=54
Henry have 54 sweets.
☆ Verification :
From above calculations we have M = 45 and N = 54
Put value of M and N in (eq 1)
\Rightarrow\:\dfrac{45}{54}\:=\:\dfrac{5}{6}⇒
54
45
=
6
5
\Rightarrow\:\dfrac{5}{6}\:=\:\dfrac{5}{6}⇒
6
5
=
6
5
Answers: 6/5 is the answere