Question

John is 7 time as old as Sarah. In 5 years’ time John will be 4 times as old as Sarah. How old is John and Sarah right now?

Answer 1

Explanation:

we shall find two simultaneous equations and then solve them. let j be John's age, and s be Sarah's age.

from the information, we have the following:

`\begin{cases}j=7s\\j+5=4(s+5)\end{cases}`

now, we use the substitution in (1) into (2).

`7s+5=4s+20\\3s=15\\s=5`

now that we have s, we can find j as
`j=5*7=35`.

Answer 2

John is currently 35 years old, and Sarah is 5 years old.

Explanation:

Let's denote John's current age as J and Sarah's current age as S.

From the given information:

1. John is 7 times as old as Sarah: J = 7S

2. In 5 years, John will be 4 times as old as Sarah: J + 5 = 4(S + 5)

We have a system of equations to solve.

Let's use substitution to find their ages:

From equation 1, we know that J = 7S.

We'll substitute this into equation 2:

(7S) + 5 = 4(S + 5)

7S + 5 = 4S + 20

7S - 4S = 20 - 5

3S = 15

S = 5

Now that we have found Sarah's age (which is 5), let's find John's age using J = 7S :

J = 7 ×5

J = 35