Question

The greater of two consecutive integers is seven less than one third the smaller integer. Find the integers.

Answer 1

Answer:

-12, -11

Step-by-step explanation:

The greater of two consecutive integers is seven less than one third the smaller integer.

x and x+1 are the two consecutive integers

x is the smallest number and x+1 is the largest number

x+1 is 7 less than 1/3 of x

$x+1= \frac{1}{3} x-7$

Now we solve for x

Combine like terms by subtracting 1/3x on both sides

$x-\frac{1}{3} x+1=-7$

$\frac{2}{3} x+1=-7$

Subtract 1 from both sides

$\frac{2}{3} x=-8$

Flip the fraction and multiply it on both sides. multiply 3/2 on both sides

$x=\frac{3}{2} x \cdot (-8)$

x=-12

The smallest integer is -12

Greatest integer is -12+1=-11

Answer 2

1st number: N (smaller number)
2nd number: N+1(greater number)

To make the equation, just put the words into their mathematical meaning
(Is: = ), (seven less: -7), [one third the smaller integer: (1/3)(N)]

(N+1)= 1/3(N)-7
Now solve:
N+1=N/3-7
N+8=(N/3)
3(N+8)=(N/3)3
3N+24=N
24=-2N
N= -12

You should probably check my math, but the equation is correct. Hopefully this helps!!