Question

Ben's age is currently twice of his sister, Emma. 8 years ago, Ben's age was 2 and a half times that of Emma's age at that time. How old is Emma now? Show all working out steps.

Answer 1

Emma is now 24 years old then Ben would be 2E, or 48 years old.

What is a system of equations?

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Let B and E be Ben's and Emma's current ages, respectively.

We have given that;

Ben's age is currently twice of his sister, Emma.

B = 2E

and

8 years ago, Ben's age was 2 and a half times that of Emma's age

B-8 = 2.5(E-8)      

We can substitute the value of B from the first equation into the last one

B-8 = 2.5(E-8)

(2E)-8 = 2.5(E-8)

2E-8 = 2.5E- 20

-0.5E = -12

E = 24

Thus, Emma is now 24 years old then Ben would be 2E, or 48 years old.

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Answer 2

Answer:

Emma is currently 24 years.

Step-by-step explanation:

Let B and E be Ben's and Emma's current ages, respectively.

We are told that:  

B = 2E [Ben's age is currently twice of his sister, Emma.]

and

B-8 = 2.5(E-8)      [8 years ago, Ben's age was 2 and a half times that of Emma's age]

We can substitute the vale of B (=2E) from the first equation into the second:

B-8 = 2.5(E-8)

(2E)-8 = 2.5(E-8)

2E-8 = 2.5E- 20

-0.5E = -12

E = 24

Emma is now 24 years old.

Ben would be 2E, or 48 years old.

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Check:

Eight years ago, they would be:

Ben = 40, and E = 16

40/16 = 2.5, which is the correct ratio of their ages 8 years ago.