MHB How Old is Lee Based on the Given Mathematical Problem?

[mathdad]

Lee has an older sister and a younger sister. Her older sister is one year more than twice Lee's age. Lee's younger sister is three years younger than she is. The sum of their three ages is 26. Find Lee's age?

My equation set up is

x + (2x + 1) + (2x + 1) - 3 = 26

This equation yields a fraction answer which is not possible in terms of age.

My answer is 27/5 as Lee's age.This cannot be right. What do you say?

 

[Euge]

Hi RTCNTC,

It's important to write down what your variables represent. If $x$ represents Lee's age, then $x - 3$, not $(2x + 1) - 3$, represents the age of Lee's younger sister. The equation is then

$$x + (2x + 1) + (x - 3) = 26$$

yielding $x = 7$.

 

[mathdad]

Hi RTCNTC,

It's important to write down what your variables represent. If $x$ represents Lee's age, then $x - 3$, not $(2x + 1) - 3$, represents the age of Lee's younger sister. The equation is then

$$x + (2x + 1) + (x - 3) = 26$$

yielding $x = 7$.

There is a typo in the application. Lee's younger sister is 3 years younger than him not the older sister. I also got x = 7. So, Lee is 7 years old.

 

[HallsofIvy]

My interpretation of the original problem is that "Lee" is a girl and the sentence "Lee's younger sister is three years younger than she is." means that the younger sister is three years younger than Lee.[FONT=MathJax_Math]R[FONT=MathJax_Main]([FONT=MathJax_Math]T[FONT=MathJax_Main]2[FONT=MathJax_Main])[FONT=MathJax_Main]⊂[FONT=MathJax_Math]R[FONT=MathJax_Main]([FONT=MathJax_Math]T[FONT=MathJax_Main])[FONT=MathJax_Math]R[FONT=MathJax_Main]([FONT=MathJax_Math]T[FONT=MathJax_Main]2[FONT=MathJax_Main])[FONT=MathJax_Main]⊂[FONT=MathJax_Math]R[FONT=MathJax_Main]([FONT=MathJax_Math]T[FONT=MathJax_Main])[FONT=MathJax_Math]R[FONT=MathJax_Main]([FONT=MathJax_Math]T[FONT=MathJax_Main]2[FONT=MathJax_Main])[FONT=MathJax_Main]⊂[FONT=MathJax_Math]R[FONT=MathJax_Main]([FONT=MathJax_Math]T[FONT=MathJax_Main])[FONT=MathJax_Math]R[FONT=MathJax_Main]([FONT=MathJax_Math]T[FONT=MathJax_Main]2[FONT=MathJax_Main])[FONT=MathJax_Main]⊂[FONT=MathJax_Math]R[FONT=MathJax_Main]([FONT=MathJax_Math]T[FONT=MathJax_Main])

 

[mathdad]

My interpretation of the original problem is that "Lee" is a girl and the sentence "Lee's younger sister is three years younger than she is." means that the younger sister is three years younger than Lee.[FONT=MathJax_Math]R[FONT=MathJax_Main]([FONT=MathJax_Math]T[FONT=MathJax_Main]2[FONT=MathJax_Main])[FONT=MathJax_Main]⊂[FONT=MathJax_Math]R[FONT=MathJax_Main]([FONT=MathJax_Math]T[FONT=MathJax_Main])[FONT=MathJax_Math]R[FONT=MathJax_Main]([FONT=MathJax_Math]T[FONT=MathJax_Main]2[FONT=MathJax_Main])[FONT=MathJax_Main]⊂[FONT=MathJax_Math]R[FONT=MathJax_Main]([FONT=MathJax_Math]T[FONT=MathJax_Main])[FONT=MathJax_Math]R[FONT=MathJax_Main]([FONT=MathJax_Math]T[FONT=MathJax_Main]2[FONT=MathJax_Main])[FONT=MathJax_Main]⊂[FONT=MathJax_Math]R[FONT=MathJax_Main]([FONT=MathJax_Math]T[FONT=MathJax_Main])[FONT=MathJax_Math]R[FONT=MathJax_Main]([FONT=MathJax_Math]T[FONT=MathJax_Main]2[FONT=MathJax_Main])[FONT=MathJax_Main]⊂[FONT=MathJax_Math]R[FONT=MathJax_Main]([FONT=MathJax_Math]T[FONT=MathJax_Main])

Well, the answer is x = 7.