Question

Solve:The greatest of three numbers is 4 times the smallest number. The middle number is 3 morethan the smallest number. The sum of the smallest and greatest number is the same as 2times the middle number.O 2,5,8O 4, 10, 16O -4,-10-16O -2,-5, -8

Answer 1

Let x represent the "smallest number" of a set of three unknown numbers.

• The greatest os 4 times the smallest, symbolically: 4x

• The middle number is three more than the smalles, symbolically x+3

• The sum of the smallest and the greatest is the same as 2 times the middle number, symbolically: x+4x=2(x+3)

Using the last expression you can clear the value of x (the smallest number)

`\begin{gathered} x+4x=2(x+3) \\ 5x=2x+6 \\ 5x-2x=6 \\ 3x=6 \\ x=(6)/(3) \\ x=2 \end{gathered}`

x=2 → The smallest number of the set of three is 2

Now using this value and the given equivalencies we can calculate the midle and greatest number:

Middle number

x+3= 2+3= 5

Greatest number

4x=4*2=8

The set of three numbers is (2, 5, 8)