The difference between two numbers is 12. If 20 is added to twice the larger number, the result is 4 more than 3 times the smaller

Question

number. Find the two numbers.

Answer 1

Hello Amy,

 

You have got two numbers X and Y that you don't know but you know that

 

X - Y = 12 so this makes  X larger than Y because the difference is positive

 

20 is added to twice the larger means 20 + 2X

 

the result (20 + 2X) IS 4 more than 3 times the smaller 4 + 3Y

 

IS means equal

 

20 + 2X = 4 + 3Y or  2X - 3Y = -16

 

The two equations are

 

X-Y = 12 or X = 12 + Y  and

 

2X - 3Y = -16

 

Substitute for X

 

2(12 + Y) - 3Y = -16

24 + 2Y -3Y = -16

24 - Y  = -16

24 + 16 = Y

40 = Y 

So Y = 40 and X = 52

 

 

 

 

 

 

 

 

 

Answer 2

Let x and y be 2 numbers.

 

1) x - y=12

 

x is the larger number.

 

2) 2x + 20=3y + 4

 

Substitute y + 12 for x in equation 2.  Solve for y.

 

2(y + 12) + 20=3y + 4

 

2y + 24 + 20=3y + 4

 

2y + 44=3y + 4

       - 4  =      - 4

2y + 40=3y

-2y        =-2y

40=y

 

Solve for x by using substitution "y + 12".

 

x=20 + 12 or 52

 

The two numbers are 40 and 52.