Q5. - Algebra 2

Question

5. If a different number is selected from each of the three sets shown below, what is the greatest sum these 3 numbers could have. 

$\text{R}=\left\{3,6,7\right\}$; $\text{S}=\left\{2,4,7\right\}$; $\text{T}=\left\{1,3,7\right\}$.

A. 13                                 B. 14

 

C. 17                                   D. 21

Step-by-Step Solution

Answer

The greatest sum of the 3 digits is 21 and the correct option is D.

Step 1 - State the definition of a variable.

A variable is a term that is used to represent an unknown value.

Here, let x be the greatest sum.

Step 2 - Evaluate the value of x .

Since the greatest sum has to be calculated, then the highest number from the three sets have to be selected.

As the sum of the highest numbers will give the greatest sum and any other number less than the highest number will not give the greatest sum.

So,

In the set $R=\left\{3,6,7\right\}$, 7 is the highest number.

In the set $S=\left\{2,4,7\right\}$, 7 is the highest number.

In the set $T=\left\{1,3,7\right\}$, 7 is the highest number.

Then, the sum of the these three numbers is:

$\begin{array}{c}x=7+7+7\\ =21\end{array}$

Step 3 - State the conclusion.

The greatest sum is 21. Therefore, option D is correct.