Q:

Write an equation to solve each problem and then solve it. In a 3-digit number, the hundreds digit is four more than the ones digit and the tens digit is twice the hundreds digit. If the sum of the digits is 12, find the three digits. Find the number.PLEASE HELP!! I DON'T GET THIS!! :(

Accepted Solution

A:
Hey there :)

Let us translate the sentences to mathematics for ease!
A 3-digit number
Ones digit → ( let p represent is )
Hundreds digit is four more than ones digit → ( 4 + p )
Tens digit is twice hundreds digit → 2 ( 4 + p ) = 8 + 2p
Sum of the digits is 12 
           ↓
Hundreds digit + Tens digit + Ones digit = 12
( 4 + p  ) + ( 8 + 2p ) + p = 12

Combine like terms
4 + 8 + p + p + 2p = 12
12 + 4p = 12

Take 12 to the opposite side { Do subtraction when you see addition }
12 ( - 12 ) + 4p = 12 - 12
4p = 0

Divide by 4 on either side
[tex] \frac{4p}{4} = \frac{0}{4} [/tex]
p = 0
( 4  + 0 ) + ( 8 + 2 ( 0 ) ) + ( 0 )

The number is 480

Check 
Hundreds + Tens + Ones = 12
4 + 8 + 0 = 12
12 = 12