Question

The sum of the two numbers is 106. The bigger number is 22 more than the smaller number. Then what is half of the smaller number?(1 Point)a) 84b) 21c) 42d) 32

Answer 1

Step 1:

In this question, we are given the following:

The sum of the two numbers is 106. The bigger number is 22 more than the smaller number. Then what is half of the smaller number?

(1 Point)

a) 84

b) 21

c) 42

d) 32

Step 2:

The details of the solution are as follows:

`\begin{gathered} Le\text{t the two numbers be x and y , such that:} \\ \text{x + y = 106 --- equation 1} \\ x\text{ + \lparen x+ 22 \rparen = 106} \\ 2x\text{ + 22 = 106} \\ \text{2x = 106 - 22} \\ 2x=84 \\ Divide\text{ both sides by 2, we have that:} \\ \text{ x =}(84)/(2) \\ \text{x = 42} \\ This\text{ means that the smaller number is 42 and} \\ The\text{ larger number is \lparen 42 + 22 \rparen = 64} \\ Then,\text{ Half of the smaller number = }(42)/(2)\text{ = 21 \lparen OPTION B \rparen} \end{gathered}`

CONCLUSION:

The final answer = 21 ( OPTION B )