The smallest of three consecutive integers is 24 less than the sum of the two larger integers. Find the three integers.

21, 22, 23

Step-by-step explanation:

Construct equations representing each piece of information.

Three consecutive integers are three numbers in a row, for example, 1, 2 and 3.

Let's let

Integer 1 = X

Integer 2 = Y

Integer 3 = Z

X = (Y + Z) - 24

We also know that

Y = X + 1

and Z = X + 2

We can now sub this information into the first equation. We do this so that we can have only one variable in the equation.

X = (X+1) + (X+2) - 24

now solve for x,

X = 2X + 3 - 24

X = 2X - 21

-X = - 21

X = 21

So, the integers are 21, 22, 23