Question

The numbers on Sam's three raffle tickets are consecutive integers. The sum of the numbers is 126. What are the numbers?

Answer 1

x + (x-1) + (x-2) = 126

x, plus the number before x, plus the number behind that
is what i have written

Answer 2

3x - 3 = 126

simplified down

can you solve from here?

Answer 3

im confused

Answer 4

well, you want three consecutive numbers that add up to 126, yes?

Answer 5

yes

Answer 6

so we have

3 consecutive numbers = 126

Answer 7

how do we write "3 consecutive numbers" with math? well, there are a couple different ways, but i chose:

x + (x-1) + (x-2)

Answer 8

x, some random number, plus the number before x, plus the number before that

Answer 9

for instance, if x = 5, then we have

x + (x-1) + (x-2)

5 + 4 + 3

3 consecutive numbers

does it make sense why i did that now?

Answer 10

and do you have to guess any number tht will sum up to 126?

Answer 11

no, here's where the clever bit comes in:

re-write "3 consecutive numbers = 126" as

x + (x-1) + (x-2) = 126

Answer 12

consecutive numbers, meaning one is bigger than another by 1
3, 4, 5
17 , 18 , 19
and so on
so,
if a number is "whatever"
whatever, whatever + 1, (whatever + 1)+1

Answer 13

now you can solve for x, and find your 3 consecutive numbers

Answer 14

so would the number that i will plug in be 3 5 and 4?

Answer 15

no, okay let's look at it step-by-step:

x + (x - 1) + (x-2)

how can we simplify this? what is the first step to collect all the terms?

Answer 16

we want to add all the x's together, and add everything that isn't an x together

Answer 17

you'd get 3 numbers that add up to 126, we dunno which they're, we do know that

whatever, whatever + 1, (whatever + 1)+1 = 126

Answer 18

but how if there aren't any other numbers, or do we start with the brackets first?

Answer 19

well, it can be re-written like this

x + x - 1 + x - 2 = 126

i just wrote it with () to make it clearer.

do you know how to simplify that down now?

Answer 20

ok one sec

Answer 21

there would be only 1 set of 3 that'd add up to that

Answer 22

i got 3x-3

Answer 23

right, remember it's equal to 126 though

3x - 3 = 126

can you solve for x now?

Answer 24

yes one sec

Answer 25

is it x=41

Answer 26

almost, you subtracted 3 instead of adding it though

3x - 3 = 126
3x - 3 + 3 = 126 + 3
3x = 129
x = 43

Answer 27

okay, if x = 43, do you know how you would find the other 2 side lengths now?

Answer 28

ooo my mistake lemme do it again

Answer 29

kk got 43 now you said how would i find the other 2 side lengths right?

Answer 30

yep, do you think you can do it?

remember, we know now that x = 43. 43 is one of the three numbers you need

remember we wrote the other two as (x - 1) and (x-2)

Answer 31

or, look at it another way:

either 43 + 44 + 45 is equal to 126, or 41 + 42 + 43 is

cause that's the only trio of numbers you can have

Answer 32

and do u guess the other 2 numbers?

Answer 33

noo, remember we had

x + (x - 1) + (x - 2) = 126?

well, we know x is 43 now, right?

so plug x back in and see what the other 2 numbers are

Answer 34

aka write it as

43 + (43 - 1) + (43 - 2) = 126

the 3 numbers should equal 126

Answer 35

oh we plug in 43 in back right ?

Answer 36

yep

Answer 37

basically:

1. create an equation with a variable
2. solve for the variable
3. use the now-solved variable to find what you need

Answer 38

kk one sec

Answer 39

kk got it thanks soo much :)