problem solving and reasoning

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azajewel

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Aug 30, 2010
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I need to know the steps to go through to solve this problem. I'm at a loss....

Tex is two years younger than his sister. In seven years, the sum of their ages will be 110. How old is Tex?
a. 85
b. 15
c. 45
d. none
 


There are different approaches, to this exercise type.

Here are some steps designed for you:

Start with the first multiple choice, and check it out.

See if it works, when you try to verify the given information (i.e., Tex's age is 2 years younger than Sis's age, and in plus 7 years for each, their ages will add up to 110).

I mean, take Tex's age and add 2 years to it. That's how you calculate Sis's age. Now advance to their future ages, by adding 7 years to each. Total those two results, and see if you get 110.

Continue through the first three choices, as needed. If and when you find a choice that works, you're done. If none of the three work out, then you're still done because the answer is then (d).

Please remind me again, are you taking a math course ?

 
Tried that...the closest I get is 101, so I think the answer is none. Am I correct? No, I am not taking a course, only trying to help my nephew with math.
 
Hello, azajewel!

Tex is two years younger than his sister.
In seven years, the sum of their ages will be 110.
How old is Tex?

. . (a) 85 . . (b) 15 . . (c) 45 . . (d) none of these
Click to expand...

When I was learning this stuff (centuries ago), I was taught a "chart" approach which got me through Word Problems.

Let \(\displaystyle x\) = Tex's age.

Since he is two years younger than Sis: .\(\displaystyle x+2\) = Sis' age.


Make a chart: one row for each person, one column for each time period.

. . \(\displaystyle \begin{array}{c||c|c|} & \text{Now} & \text{Then} \\ \hline\hline \text{Tex} & x & \\ \hline \text{Sis} & x+2 & \\ \hline \end{array}\)

"Then" is 7 years from now; both will be 7 years older.
. . Tex will be \(\displaystyle x+7\) years old.
. . Sis will be \(\displaystyle x+2+7 \:=\:x+9\) years old.


Write those into the chart.

. . \(\displaystyle \begin{array}{c||c|c|} & \text{Now} & \text{Then} \\ \hline\hline \text{Tex} & x & x+7 \\ \hline \text{Sis} & x+2 & x+9\\ \hline \end{array}\)


We are told that the sum of their ages (then) will be 110.

There is our equation: .\(\displaystyle (x + 7) + (x+ 9) \;=\;100\)

And we get: .\(\displaystyle 2x+16 \:=\:110 \qiad\Rightarrow\quad 2x \:=\:94 \quad\Rightarrow\quad x \:=\:47\)

Therefore, Tex is 47 years old (now).

 
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