Age problems are “classic” word problems. Find a solution and set up an equation to model each situation.
a. Abigail is 6 years older that Jonathan. Six years ago she was twice as old as he. How old is each now?
Let's set up variables to represent Abigail's and Jonathan's current ages.
Let A be Abigail's current age.
Let J be Jonathan's current age.
From the given information, we can set up the following equations:
1) Abigail is 6 years older than Jonathan, so A = J + 6.
2) Six years ago, Abigail was twice as old as Jonathan. So, six years ago Abigail's age was A - 6, and Jonathan's age was J - 6. The equation for this scenario is A - 6 = 2*(J - 6).
To find the current ages, we need to solve the system of equations formed by equations (1) and (2).
Substituting equation (1) into equation (2), we have:
(J + 6) - 6 = 2*(J - 6)
J = 2J - 12 - 6
J = 2J - 18
18 = 2J - J
J = 18
Substituting J = 18 into equation (1), we can find Abigail's age:
A = J + 6
A = 18 + 6
A = 24
Therefore, Abigail is 24 years old and Jonathan is 18 years old.