Two numbers sum to 56. thrice the first subtracted from the second is 4. find the numbers?

1 Answer

Answer:

The two numbers are #13# and #43#.

Explanation:

There are two numbers. Let's call them #x# and #y#.

#x + y = 56#

Thrice the first subtracted, so #-3x#, from the second, #y#, is #= 4#, so

#y - 3x = 4#

Now you have a simultaneous equation to work with.

#y + x = 56#

#y - 3x = 4#

Same signs subtract, Different signs add. I always prefer dealing with the number after the operation, so I'll start with that. We should make the coefficients the same.

#3(y+x) = 3(56)#
#y - 3x = 4 #

#3y + 3x = 168#
#y - 3x = 4#

If we add the bottom to the top, we end up with

#4y = 172#

#y = 172/4#

#y = 43#

Substitute your answer for #y# into any of the equations given (and never the one that you made, in case it is wrong).

Let's take the given one.

#x + y = 56#

#x + 43 = 56#

#x = 56-43#

#x = 13#

Therefore,

#{(x = 13), (y = 43) :}#