Jerry's age is 9 years less than 7 times Tom's age. The sum of their ages is 39. Solve algebraically to find each person's age.

Answer 1

Hi Disha,

Let's start by assigning variables to Jerry and Tom. We'll use 'J' to represent Jerry's age and 'T' to represent Tom's age.

We know that Jerry is 9 years less than 7 times Tom's age. We can represent this in the following way.

J=(7*T)-9

We also know that the sum of Jerry and Tom's ages is 39. This can be represented by

39=J+T

We can now isolate Tom's age in the second equation by subtracting Jerry's age from both sides like so.

39-J=T

Now that we have Jerry's age isolated, we can substitute this into the first equation we derived in order to have an equation with only one variable.

J=(7*(39-J))-9

This equation can be solved in order to determine Jerry's age.

J=273-7J-9

J=264-7J

8J=264

J=33

We find that Jerry is 33 years old, but the question asks you to determine each person's age. We know that the sum of their ages is 39, so we can find Tom's age by subtracting Jerry's age (33) from 39 and this implies that Tom is 6 years old.

T=6

J=33

We can check our solution by confirming that Jerry is 9 years less than 7 times Tom's age.

6*7=42-9=33

Hope this helps!

Best,

Joel