Three consecutive even intergers are such that 5 times the greatest decreased by half the sum of the two smallest results in 195. What is the middle number

Answer 1

x = first integer

x+2 = second integer

x+4 = third integer

5(x+4) - (x+2+x)/2 = 195

10(x+4) -(2x+2) = 390

10x + 40 -2x - 2 = 390

8x + 38 = 390

8x = 352

x = 44

middle on is x+2 = 46

Answer 2

Let 2x, 2x+2 and 2x+4 be the 3 even consecutive numbers, where x is an integer

5(2x+4) - (1/2)(2x+2x+2) = 195

10x+20 - 2x-1 = 195

8x = 195-19 = 176

x = 176/8 = 22

2x + 44

2x+2 = 44+2 = 46 = the middle number

Answer 3

We'll assume the first integer to be X.

the numbers are even, which means they are 2 numbers apart

so the three numbers are X , (X+2) , and (X+4)

5 times the greatest is 5(X+4)

decreased means we are going to subtract

half the sum of the smallest means we'll add the smaller numbers and half it

that's ¹_/2 [X + (X+2)]

so 5(X+4) - ^1/₂ (X+X+2) = 195

now let's solve

5X + 20 - ^1/₂ (2X+2) = 195

5X + 20 - X -1 = 195

4X + 19 = 195

4X = 176

X = 44

the middle was x+2 so that 44+2 = 46

so the answer is 46