four consecutive integers the sum of the first integer and third integer is the same value as four less than three times the fourth integer.What is the value of

Question

There exist four consecutive integers such that the sum of the first integer and the third integer has the same value as four less than three times the fourth integer. What is the value of the second integer

 

 

Answer 1

pick a variable for your first integer, say a

four consecutive integers are then a, a+1, a+2, a+3

 

make an equation from the words

sum of first integer and third integer: a + a+2

four less than three times the fourth integer: 3(a+3) - 4

 

a + a + 2 = 3(a+3) - 4   combine like terms on the left side, distribute on the right

2a+2=3a+9-4                combine like terms on the right side

2a+2=3a+5                   take away 2a from both sides

2=a+5                          take away 5 from both sides

-3=a

 

So the first integer is -3, so the second integer is -2.