Question

The sum of two numbers is 60. Their difference is 12. What is the smaller number?

Answer 1

okay so with this information we can write down some expressions.

Answer 2

"the sum of two numbers is 60"

Answer 3

"sum" means addition

Answer 4

so that sentence means:
Some number plus another number equals 60.

Answer 5

"some number" + "another number" = 60
in math, to simplify things we can represent "some number" and "another number" with letters. I like to use x and y:

x + y =60

Answer 6

"Their difference is 12."
Difference usually refers to subtraction.
So that sentence means "the difference of some number and another number is 12"
or
x - y =12

Answer 7

so now we have:
x - y = 12
x + y = 60

Answer 8

do you know of a way to figure out what x or y is?

Answer 9

No I dont

Answer 10

we can use a method called substitution.

Answer 11

lets start with the top equation

Answer 12

x - y = 12

Answer 13

if you add y to both sides what do you get?

Answer 14

24

Answer 15

x - y = 12
x = 12 + y

Answer 16

do you see how i did that?

Answer 17

oh yes

Answer 18

okay so now we know for sure that x equals "12 + y"

Answer 19

yes

Answer 20

well that means that we can go back to our other equation and plug "12 + y" in for "x"

Answer 21

yes

Answer 22

x = "12 + y"
and from before,
x + y = 60
that means that
"12 + y" + y = 60

Answer 23

(usually in math we dont write quotes, instead we use parenthesis)

(12 + y) + y = 60
12 + y + y =60

Answer 24

if i have y + y how many y's do I have?

Answer 25

24

Answer 26

y + y = ??

Answer 27

12

Answer 28

y + y = 2y

Answer 29

one y plus another y is two y's

Answer 30

=P

Answer 31

12 + y + y =60
12 + 2y = 60

Answer 32

So Wat Would The Smaller number be?

Answer 33

well we gotta figure out x and y to know which one is smaller
useing this you can figure out y!
12 + 2y = 60

Answer 34

minus 12 from both sides

Answer 35

then divide both sides by 2

Answer 36

what do you get for y?

Answer 37

y = 24
x + y = 60
x + 24 = 60
x = 36

Answer 38

the smaller one is 24