Adam and Ben

When Ben reaches Adam's current age, Adam will be 23 years old. When Adam was Ben's current age, Ben was 2 years old. How old are Ben and Adam today?

Final Answer:

a =  16
b =  9

Step-by-step explanation:


b+x = a
a+x = 23
a-y = b
b-y = 2

a-b-x = 0
a+x = 23
a-b-y = 0
b-y = 2

Row 2 - Row 1 → Row 2
a-b-x = 0
b+2x = 23
a-b-y = 0
b-y = 2

Row 3 - Row 1 → Row 3
a-b-x = 0
b+2x = 23
x-y = 0
b-y = 2

Row 4 - Row 2 → Row 4
a-b-x = 0
b+2x = 23
x-y = 0
-2x-y = -21

Pivot: Row 3 ↔ Row 4
a-b-x = 0
b+2x = 23
-2x-y = -21
x-y = 0

Row 4 - 1/-2 · Row 3 → Row 4
a-b-x = 0
b+2x = 23
-2x-y = -21
-1.5y = -10.5


y = -10.5/-1.5 = 7
x = -21+y/-2 = -21+7/-2 = 7
b = 23-2x = 23-2 · 7 = 9
a = 0+b+x = 0+9+7 = 16

a = 16
b = 9
x = 7
y = 7

Our linear equations calculator calculates it.
b=9



Help us improve! If you spot a mistake, please let let us know. Thank you!







Tips for related online calculators
Do you have a system of equations and are looking for calculator system of linear equations?
Do you want to convert time units like minutes to seconds?

You need to know the following knowledge to solve this word math problem:

algebrabasic operations and conceptsUnits of physical quantitiesGrade of the word problem

Related math problems and questions: