Question

There are two numbers which sum to 23. If one number is seven less than four times the other, find the numbers.

Answer 1

@AZ

Answer 2

So let's call one number 'x' and the other number 'y'

Does that sound good to you?

Answer 3

yep

Answer 4

so it says the two numbers have a sum of 23

that means when we add the two numbers we get 23

how can we write that with x and y

Answer 5

x + y = 23

Answer 6

Excellent!

Answer 7

now we have to write an equation for the other sentence as well

one number is seven less than four times the other

the way I like to think about it is
change the word `is` to an `=` sign

when we say less than, what we doing? is that addition/subtraction/multiplication/division

Answer 8

subtraction

Answer 9

x = 7 - 4 * y

Answer 10

you almost had it

but when we say 7 less than (something)

that means it's (something) - 7

Answer 11

so x = 4y - 7

does that make sense?

Answer 12

yep

Answer 13

so we have two equations now

x + y = 23
x = 4y - 7

let me add colors so you can see how you can plug one equation into the other

Answer 14

\(\color{red}{x} + y = 23\)

\(\color{red}{x} = \color{red}{4y - 7} \)

so do you see how we have an x in the first equation?
and in the second equation, we say x = something

if x is equal to that, then that means we can replace x with that something

so you can plug that red part into the first equation

Answer 15

do you see how can you replace it? since they're equal

Answer 16

yep

Answer 17

whats the next step

Answer 18

just solve it

4y -7 + y = 23

solve for y

Answer 19

-3y+y=23

Answer 20

no no no
how'd you get that

you have 4 apples and you add another apple, how many apples?

think of the y as an apple

4y + y = ??

Answer 21

6y

Answer 22

are you sure?

you have 4 apples and I give you 1 more apple. How many apples do you have now?

Answer 23

5y

Answer 24

there we go!

Answer 25

so
4y -7 + y = 23

now we get

5y - 7 = 23

add 7 on both sides, what do you get

Answer 26

12y=30

Answer 27

Remember 5y is our apples
7 is just a number

Can you add apples and numbers together?

No we can't.

So when we add 7 on both sides

5y - 7 + 7 = 23 + 7

-7 + 7 gets us 0 and so we're left with

5y = 30

Answer 28

so can you solve for y now?

Answer 29

5 * 6 = 30

Answer 30

so what is y

Answer 31

y=6

Answer 32

Good! Now let's find x and we'll be all done

remember we said that the two numbers add up to 23

if one number is 6, what's the other number?
what number plus 6 gives us 23

Answer 33

17+6=23

Answer 34

so what are you two numbers going to be?

Answer 35

6,17

Answer 36

and that's your answer!

Answer 37

thanks

Answer 38

You're welcome!