Algebra Word Problem 2 Calculator sets up and solves a classic age word problem, comparing two people's current ages and projecting both ages forward by a stated number of years. Enter two current ages, and optionally a number of years into the future, to see the age relationship worked out algebraically.
Define variables for an age problem
Age word problems compare two quantities that both increase at the same rate over time: one year older for one person means one year older for the other too. Let A represent the first person's current age and B represent the second person's current age.
Algebra Word Problem 2 Calculator names these explicitly as variables before computing anything, since a clear variable definition is what keeps a multi-step age problem from becoming confusing.
Compute the age difference
The difference between two people's ages never changes over time, since both ages increase by the same amount each year. If A is 34 and B is 27, the difference A − B is 7, and that gap of 7 years stays fixed whether the comparison happens today, in 5 years, or 5 years ago.
Algebra Word Problem 2 Calculator reports this difference as a standing fact that carries through the rest of the problem.
Project both ages forward
Given a number of years, say 6, both ages increase by that same amount: A + 6 and B + 6. For A = 34 and B = 27, in 6 years the ages become 40 and 33.
The difference between the projected ages is still 40 − 33 = 7, confirming that projecting forward preserves the original gap, which is a useful check on any age-problem calculation.
Work through a classic ratio-based age problem
A common age problem states a current relationship and a future ratio: "A is 34, B is 27; in how many years will A be exactly 1.25 times B's age?" Set up the equation A + n = 1.25(B + n), or 34 + n = 1.25(27 + n).
Expand the right side: 34 + n = 33.75 + 1.25n. Subtract n from both sides: 34 = 33.75 + 0.25n. Subtract 33.75: 0.25 = 0.25n, so n = 1. Checking: in 1 year, A is 35 and B is 28, and 35 divided by 28 is exactly 1.25.
Work through a sum-and-difference age problem
A different classic format gives the sum of two ages and their difference, asking for each age individually. If two ages sum to 58 and differ by 12, let A be the older and B the younger: A + B = 58 and A − B = 12.
Adding these two equations directly eliminates B: 2A = 70, so A = 35. Substituting back, B = 58 − 35 = 23. Checking both conditions: 35 + 23 = 58 and 35 − 23 = 12, confirming the solution.
Interpret a negative number of years correctly
When a solved value of n comes out negative in a future-ratio age problem, it usually means the stated ratio held at some point in the past rather than the future. If solving for "when will A be twice B's age" gives n = −4, that indicates A was twice B's age 4 years ago, not 4 years from now.
Algebra Word Problem 2 Calculator reports the signed value of n directly so this past-versus-future distinction stays visible rather than being hidden by an assumption that n must be positive.
Avoid this common mistake
A frequent error adds the same number of years to only one person's age while leaving the other unchanged, which breaks the fundamental rule that time passes equally for both people in the problem. Whatever number of years is added to A's current age must be added to B's current age too, since both people age together.
Algebra Word Problem 2 Calculator always projects both ages by the identical number of years to avoid this asymmetry.
Frequently asked questions
How do you set up an age word problem algebraically?
To set up an age word problem, assign a variable to each person's current age, express the stated relationship as an equation using those variables, and add the same unknown or given number of years to both ages when the problem asks about the future.
Does the age difference between two people ever change?
The age difference between two people never changes over time, since a year added to one person's age is also a year added to the other's, keeping their gap constant no matter how far forward or backward the comparison moves.
How do you solve for how many years until one age is a multiple of another?
To solve for how many years until one age is a specific multiple of another, set up the equation (age 1 + n) = multiple × (age 2 + n), expand the right side, collect the n terms on one side, and solve for n directly.
What if the calculated number of years is negative?
A negative number of years in the solution generally means the described age relationship held in the past rather than the future; interpreting a negative n as "that many years ago" often makes the answer meaningful again.
Can this method handle more than two people?
This substitution-based method as described solves a two-person, two-variable relationship directly; a three-person age problem needs an additional independent equation relating the third person's age before it reduces to a solvable system.
How do you solve an age problem given a sum and a difference?
To solve an age problem given a sum and a difference, add the sum equation and the difference equation together to eliminate one variable directly, solve for the remaining variable, then substitute back to find the other one.
Why does adding the sum and difference equations eliminate a variable?
Adding the sum equation (A + B) and the difference equation (A − B) eliminates B because +B and −B cancel exactly, leaving 2A on its own, which is a standard elimination technique for any two-equation, two-unknown linear system.
Summary
Algebra Word Problem 2 Calculator defines two current ages as variables, computes their fixed difference, and projects both ages forward by the same number of years to solve relationship-based age problems.
Enter two current ages and, when needed, a target ratio or number of years, to see the equation set up, expanded, and solved with a check against the original relationship.