Question 1102068: The sum of john and jasmin is 4 times as old as john. What is their age?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let x = john's age.
let y = jasmine's age.
x + y = 4x
solve for y to get y = 3x.
no matter how old john is, jasmine will be 3 times as old, and the sum of their ages will be 4 times john's age.
for example:
if john is 1 years old, then jasmine is 3 years old and the sum of their ages is 4 which is 4 times john's age.
if john is 5 years old, then jasmine is 15 years old and the sum of their ages is 20 which is 4 times john's age.
you cannot determine john's age from this formula because john could be any age between any number greater than 0 and some finite number such as the maximum age that jasmine can be.
for example:
if john is 1/3 years old, then jasmine is 1 year old and the sum of their ages is 4/3 which if 4 times john's age.
what you have is a system of equations where the result is 0 = 0.
this means you have an infinite number of possible solutions.
consider.
x + y = 4x
y = 3x
that's your system of equations that has to be solved simultaneously.
rearrange the equations as follows:
start with x + y = 4x
subtract 4x from both sides of the equation to get -3x + y = 0
start with y = 3x
subtract 3x from both sides of the equation to get -3x + y = 0
they're the same equation which results in an infinite number of solutions.
any solution of the first equation is also a solution of the second equation.
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