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? (Only 1 choice of answer)

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

Answer 1

C x + 5 =(5 - x) - 5

Explanation:

Answer 2

x + 5 = (x + 5) - 5, which has no solution ⇒ answer C

Explanation:

* Lets study the situation in the problem

- Jessica is 5 years older than her sister Jenna

- After five years Jenna's age will be as old as Jessica was five years ago

- Jenna's age now is x

* Lets change all information above to equation

∵ Janna's age now is x

∵ Jessica is 5 years old than Janna

∴ The age of Jessica now is x + 5

- After 5 years Janna's age will be add by 5 years

∵ Her age now is x

∴ Her age after 5 years will be x + 5

- From 5 years ago Jessica's age was her age now mins 5 years

∵ Her age now is x + 5

∴ Her age from 5 years ago is (x + 5) - 5

∵ Janna's age after 5 years = Jessica age from 5 years ago

∴ x + 5 = (x + 5) - 5

- Lets solve the equation to know how many solution

∵ x + 5 = x + 5 - 5 ⇒ add the like terms

∴ x + 5 = x ⇒ subtract x from both sides

∴ 5 = 0

- But 5 ≠ 0, the two sides of the equation not equal each other

∴ There is no solution for this equation

* The equation is x + 5 = (x + 5) - 5, which has no solution