Question

Find a number whose product with 6 is the same as its sum with 60. (Hint: you may want to try guess and check or a table.) Be sure to check your answer for reasonableness.

Answer 1

Do you understand how to turn word problems into equations?

Answer 2

no

Answer 3

we are looking for a number
in the end it'll be 6, or -3 or even 0
we just don't know yet
so, until we do we'll call it x

Answer 4

OK with that idea?

Answer 5

yes

Answer 6

We know something about x
we know that if we add 6 to it, we will have x + 6

Answer 7

sorry add 60

Answer 8

Do you understand that?

Answer 9

o ok so it would be 60x

Answer 10

add 60 will give x + 60
multiply by 6 will give 6x

Answer 11

o ok

Answer 12

really OK?
The last fact we're given is that if add 60 to get x + 60
and separately, multiply by 6 to 6x
those two new numbers are equal!

x + 60 = 6x

Answer 13

ok

Answer 14

Do you know how to work with that equation so that it will be come
x = something

Answer 15

no i need help with that too

Answer 16

The basic rule for equations is simple: do the same thing to both sides and you still have a valid equation.

x + 60 = 6x

what should we do?

Answer 17

subtract 6 from both sides

Answer 18

x + 60 - 6 = 6x - 6
x + 54 = 6x - 6
is it getting simpler?

Answer 19

yes

Answer 20

Nooooooo

Answer 21

Try subtracting x from both sides. After all, it's just a number

Answer 22

6+54=6

Answer 23

Back to the original, I mean:
x + 60 = 6x
x + 60 - x = 6x - x
60 = 5x
is that simpler?

Answer 24

yea i quess

Answer 25

It looks simpler to me.
What we did is isolating x on one side.
Next we'll multiply both sides by something.
What should it be?

Answer 26

60 = 5x
60 (1/5) = 5x (1/5) = x
x = 12
Check your work.
Is 12 + 60 = 6(12) ???

Answer 27

Gotta go. HTH