Find three consecutive integers such that the first increased by twice the second is 24 more than the third.

12, 13, 14

Step-by-step explanation:

Let the smallest of the three integers be x.

The difference between an integer and the next greater one is 1.

Then the next greater one is x + 1, and the greatest one of all is x + 2.

Now we translate each piece of the given information until we find an equation.

"the first increased by twice the second"

x + 2(x + 1)

"is"

=

"24 more than the third"

x + 2 + 24

Put all three pieces together, and you get the equation:

x + 2(x + 1) = x + 2 + 24

Now we solve the equation for x, the smallest of the three integers.

x + 2x + 2 = x + 26

3x + 2 = x + 26

2x = 24

x = 12

The smallest integer is 12.

x + 1 = 12 + 1 = 13

x + 2 = 12 + 2 = 14

The other two integers are 13 and 14.

12, 13, 14

Now, we check the answer with the given information.

"the first increased by twice the second"

12 + 2 * 13 = 12 + 26 = 38

The first increased by twice the second is 38.

"24 more than the third"

14 + 24 = 38

24 more than the third one is 38.

38 = 38

Our solution is correct.

multiple all that

step-by-step explanation:

27×17