Question

The sum of the ages of John and Sarah is 26. Five years ago, John was three times as old as Sarah. How old is John now?

Answer 1

To find John's current age, we can set up a system of equations using the given information and solve for the variables.

Step-by-step explanation:

To solve this problem, we can set up a system of equations to represent the given information:

Let's assume John's age is x and Sarah's age is y. We know that the sum of their ages is 26, so we can write the equation:

x + y = 26

Five years ago, John's age would have been x - 5, and Sarah's age would have been y - 5. We also know that John's age was three times Sarah's age at that time, so we can write another equation:

x - 5 = 3(y - 5)

We can solve this system of equations to find the values of x and y. Once we find the values, we will know John's current age.

Answer 2

By setting up a system of equations using the given information, we find that John is currently 18 years old.

Step-by-step explanation:

To find John's current age, let's set up a system of equations based on the information provided. Let J represent John's age now, and S represent Sarah's age now.

We are given that the sum of the ages of John and Sarah is 26, so our first equation is:

J + S = 26

Five years ago, John was three times as old as Sarah. This gives us our second equation:

J - 5 = 3(S - 5)

Rearrange the second equation to solve for J:

J = 3S - 10 + 5

J = 3S - 5

Now we can substitute the value of J from the first equation:

(26 - S) = 3S - 5

Adding 5 to both sides and then adding S to both sides gives us:

31 = 4S

Dividing both sides by 4 gives us:

S = 7.75

Since ages are typically whole numbers, let's round Sarah's age to the nearest whole number, which is 8. Now we substitute the value of S back into the first equation to find J:

J = 26 - 8

J = 18

So, John is currently 18 years old.