Sarah and Henry share some sweets in the ratio 5:6 Sarah eats 24 of her sweets and the ratio of sweets left becomes 1:2 .
how many sweets did Henry have ?

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

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.

im with everythinglos so yeahhhhh

step-by-step explanation: