Question

One year ago, Deon was 15 times as old as Penelope. In 3 years, Deon will be the square of Penelope's age. Which equation would we use to solve for Deon's age?​

Answer 1

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Let Patrick's age be x.

John's age is 3x+15 because it is 15 more than 3 times Patrick's age which is x.

If the sum of their ages is 45, and we know that Patrick is x and John is 3x+15, we add them together to get:

4x+15=45

Now we find out what x is so we take 15 from each side of the equation.

We now have:

4x=30

Divide each side of the equation by 4.

We now have:

x=7.5

Since Patrick's age was x then that means he is 7.5.

Now to get John's age we make x=7.5 and input that in the equation:

3x+15

This is (3×7.5) +15

If we work this out we are left with

22.5+15.

This equals 37.5.

Their respective ages are 37.5 and 7.5.

Hope this helps and good luck. :=)

Answer 2

SOLUTION

GIVEN

• One year ago, Deon was 15 times as old as Penelope.

• In 3 years, Deon will be the square of Penelope's age.

TO DETERMINE

The equation would we use to solve for Deon's age

EVALUATION

Let one year ago -

Age of Penelope = x years

Then age of Deon = 15x years

At present -

Age of Penelope = x + 1 years

Then age of Deon = 15x + 1 years

After 3 years

Age of Penelope = x + 1 + 3 = x + 4 years

Then age of Deon

= 15x + 1 + 3 years

= 15x + 4 years

By the given condition

$\sf \: 15x + 4 = {( x+ 4)}^{2}$

Which is the required equation we would use to solve for Deon's age

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