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.
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?
1 answer
1 answer