Find four consecutive integers such that 8 times the sum of the first and the third is 40 greater than 10 times the fourth.

An integer number is a Whole number which must not have any decimal. For example -5, -4, -3 -2, -1, 0, 1 2, 3, 4, 5. So an integer can be negative and positive.

Following are the formulas for calculating Even and Odd integers:

Let the even number be = X

consecutive even integers =  X, X + 2, X + 4, X + 6...etc

Odd number integer will be = 2X + 1

Consecutive Odd Integer numbers = (2X+ 1), (2X + 1+ 2), (2X+ 1+2+2)and so on.

Now the answers:

Four consecutive even integers such that the sum of the first and third is 6 less than the largest : Answer is -4, -2, 0, 2

Equation X + X + 2 = (X + 6) - 6

four consecutive odd integers such that the largest equals 2 more than the sum of the other three:  Answer -1, 1, 3, 5

Equation 2X+7 = (2X+1) + (2X+3) + (2X+5) + 2

Two consecutive even integers such that twice the smaller is 26 less than three times the larger: Answer 20, 22

The consecutive integers such that twice the sum of the first and second is 27 more than three times the Third: Answer 31, 32, 33

Three consecutive integers such that three times the smallest added to 7 is 13 less than four times the largest: Answer 12, 13, 14

Three times the first of three consecutive integers is subtracted from twice the second the result is 16 more than the third the integers: Answer 8, 9, 10

Four cons ecutive even integers so that the sum of the first two added to twice the sum of the last two is equal to 742: Answer 120, 122, 124, 126

The smallest of three consecutive odd integers is added to four times the largest IT produces a result 729 more than four times the middle integer. find the numbers: Answer 721, 723, 727

Three consecutive multiples of 5 have a sum of 75 what are the numbers: Answer 20, 25, 30

Learn More: link

An integer number is a Whole number which must not have any decimal. For example -5, -4, -3 -2, -1, 0, 1 2, 3, 4, 5. So an integer can be negative and positive.

Following are the formulas for calculating Even and Odd integers:

Let the even number be = X

consecutive even integers =  X, X + 2, X + 4, X + 6...etc

Odd number integer will be = 2X + 1

Consecutive Odd Integer numbers = (2X+ 1), (2X + 1+ 2), (2X+ 1+2+2)and so on.

Now the answers:

Four consecutive even integers such that the sum of the first and third is 6 less than the largest : Answer is -4, -2, 0, 2

Equation X + X + 2 = (X + 6) - 6

four consecutive odd integers such that the largest equals 2 more than the sum of the other three:  Answer -1, 1, 3, 5

Equation 2X+7 = (2X+1) + (2X+3) + (2X+5) + 2

Two consecutive even integers such that twice the smaller is 26 less than three times the larger: Answer 20, 22

The consecutive integers such that twice the sum of the first and second is 27 more than three times the Third: Answer 31, 32, 33

Three consecutive integers such that three times the smallest added to 7 is 13 less than four times the largest: Answer 12, 13, 14

Three times the first of three consecutive integers is subtracted from twice the second the result is 16 more than the third the integers: Answer 8, 9, 10

Four cons ecutive even integers so that the sum of the first two added to twice the sum of the last two is equal to 742: Answer 120, 122, 124, 126

The smallest of three consecutive odd integers is added to four times the largest IT produces a result 729 more than four times the middle integer. find the numbers: Answer 721, 723, 727

Three consecutive multiples of 5 have a sum of 75 what are the numbers: Answer 20, 25, 30

Learn More: link

These are indeed quite a lot of exercises, but a lot of them are almost identical - only small computations will change. So, I'm glad to help you with one exercise from every cathegory, but I encourage you to solve the others on your own.

You can call four consecutive integers as

So, the sum of the first and third is

We want this quantity to be six less than the largest, i.e.

So, the equality is

Subtract x from both sides:

Subtract 2 from both sides:

So, the consecutive integers are

In fact, the sum of the first and third is , which is indeed six less than the largest:

If you call the first odd number , the next consecutive odd numbers will be

In fact, we have to count skipping two's, because we only want odd integers. From here, you go on like exercise 1: you write the largest (which is x+6), and set it to be two more than the sum of the other three (x, x+2 and x+4)

By the same logic of exercise 2, two consecutive even integers are , assuming that x is even.

So, you set the equation as usual: the smaller (which is x) is 26 less than three times the larger (which means 3(x+2)-26)

These are all pretty identical to exercise 1: you start by listing three or four consecutive integers:

and then you translate the request of each exercise accordingly. Remember that expressions like "three times the second number" means that you have to multiply: , while expression like "six more than the first" or "thirteen less than the first" imply adding/subtracting: or .

A multiple of 5 can be written as , for some integer k.

So, three consecutive multiples of 5 are

We want these three numbers to have a sum of 75. So, we have

So, the three numbers are

Step-by-step explanation:

-8-10,-12-14

-8 plus -12 is -20

-20 times 5 is -100

-14 times 8 is -112

-100 is 12 more than -112

-8-10,-12-14

-8 plus -12 is -20

-20 times 5 is -100

-14 times 8 is -112

-100 is 12 more than -112

Step-by-step explanation:

-8-10,-12-14

-8 plus -12 is -20

-20 times 5 is -100

-14 times 8 is -112

-100 is 12 more than -112