Question

Jessica is 5 years older than her sister Jenna. Jenna tells her sister that in 5 years, she will be as old as Jessica was 5 years ago. If Jenna’s age is x, which equation represents the situation? How many solutions does the equation have?

A.
x + 5 = (5 − x) − 5, which has one solution
B.
x + 5 = (x + 5) − 5, which has infinitely many solutions
C.
x + 5 = (x + 5) − 5, which has no solution
D.
x + 5 = (5 − x) − 5, which has infinitely many solutions
E.

Answer 1

Jenna's age Jessica's age

today x x + 5

in 5 years x+5

5 years ago x + 5 - 5

Equality x + 5 = x + 5 - 5

=> x + 5 = x

The equation is x + 5 = x

That equation has not any solution, because it reduces to 5 = 0, which is an absurd.

So, the conclusion is that information given by Jenna is wrong.

It is logical: if the difference of the ages is 5, in five years Jenna will have 10 years more than what her sister had 5 years ago, no 5 as she told Jessica.

Answer 2

(x + 5) + 5 = (x + 5) + 5, which has infinitely many solutions

Explanation: