SAT PREP 2015

Question

Twice the sum of two consecutive integers is 10 less than 5 times the smaller integer. Find the greater integer.

Answer 1

Call the smaller consecutive integer X

Then the greater is    X+1

 

The sum of these integers is X+(X+1)  =  2X +1

Twice the sum is               2(2X+1)      = 4X+2

 

10 less than 5 times smaller                 = 5X-10

 

So                                 5X-10            =   4X  +2

                                                    X    =    12

 

Therefore the greater integer    X+1      =   13

 

 

Answer 2

Let x be the smaller integer.

 

Since they're consecutive, the larger one must be x + 1.

 

"Twice the sum of two consecutive integers" is 2(x + x + 1) = 2(2x + 1) = 4x + 2

 

"10 less than 5 times the smaller integer" is 5x - 10

 

So...

 

4x + 2 = 5x - 10

2 = x - 10

12 = x

 

So 12 is the smaller integer, which means that 13 is the larger one.