Question

Need help with the consecutive integer one

Answer 1

Answer: the four numbers are 17, 18, 19, and 20

17+18+19+20 = 74

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How I got this answer:

Consecutive integers are whole numbers that follow one after the other. One example would be 6, 7, 8, 9. We want to find four of these numbers such that they add to 74. Going off the example, adding 6,7,8,9 leads to 6+7+8+9 = 30 which is too small. Trying 7,8,9,10 leads to 7+8+9+10 = 34 which is again too small. We might be here a while if we use this method of guess-and-check.

Instead it is much better to use algebra. We don't know the first number, so let's call it x. The next number right after that is x+1. Then there's x+2 and finally x+3

first number = x

second number = x+1

third number = x+2

fourth number = x+3

Add them all up. Combine like terms

(first)+(second)+(third)+(fourth) = (x)+(x+1)+(x+2)+(x+3)

(first)+(second)+(third)+(fourth) = x+x+1+x+2+x+3

(first)+(second)+(third)+(fourth) = (x+x+x+x)+(1+2+3)

(first)+(second)+(third)+(fourth) = 4x+6

Add up x, x+1, x+2, x+3 leads to 4x+6

Set this expression equal to 74 which is the target sum we want. Solve for x

4x+6 = 74

4x+6-6 = 74-6 .... subtract 6 from both sides

4x = 68

4x/4 = 68/4 .... divide both sides by 4

x = 17

Now we can say the following

first number = x = 17

second number = x+1 = 17+1 = 18

third number = x+2 = 17+2 = 19

fourth number = x+3 = 17+3 = 20

The four consecutive numbers are 17, 18, 19, 20

To check we have the right answer, add them up: 17+18+19+20 = 74 and we get the proper sum we want. This confirms the answer.