math question?

Question

please, i know this is a simple question but i need help,

the sum of two numbers is 141. one number is 37 more than the other . find the numbers.

the other questions is

find two numbers whose sum if 54 and whose difference is 28.

please help me figure the problems, and explain how to do it, thanks

Answer 1

1)
Let the two numbers be x and (x + 37)

x + (x + 37) = 141
2x + 37 = 141
2x = 104
x = 52
x + 37 = 89

The two numbers are 52 and 89
-----------------
2)
Let the lower number be x and the higher number be x + 28
x + (x + 28) = 54
2x + 28 = 54
2x = 26
x = 13
x + 28 = 41

The two numbers are 13 and 41

Answer 2

let the two number be x and y
x + y = 141
and y = x + 37

by substitution, x + x + 37 = 141
2x = 104
x = 52 y=89

x + y = 54
x - y = 28
2x = 82
x = 41 y= 13

Answer 3

(a)
lets make the first number i x and the second one is y
so.. x+y =141 -->x=141-y (1st equation)
x is 37 more than y, so x=y+37(2nd equation)
then you substitute the x in the first equation to the second :
141-y = y+37
104 = 2y
y= 52 then put in the 1st equation.
x= 141-52
x= 89
that means the 1st number is 89 and the 2nd one is 52

(b)
this works the same way as (a) does
1st# = x
2nd# = y
x + y = 54 , and x - y = 28
x + y = 54 --> x = 54-y (put into the 2nd equation to substitute x)

x - y = 28
(54-y)-y = 28
54-2y=28
26=2y
y=13 --> that gives x=41
the 1st# is 41 and the 2nd one is 13 (tada!!)
54 - y

Answer 4

let x = the first number
x+37 = second number

x + (x+37) = 141
minus 37 on both sides.
2x = 104
divide by 2.
x = 52
that means the first number equals 52, and the second is 52 + 37, which is 89.

let x = first number
x + y = 54
x - y = 28
for this equation you have do do something called systems, i think? i cant remember the name.
line up the two equations, and you can see the 2 y's cancel out. (+y, -y)
so you have 2x = 82
divide by 2, it equals 41.
so you have x = 41.
plug x into any of the two equations.
lets take, x + y =54.
41 + y =54
minus 41 on both sides.
y=13

41 & 13 are the two numbers.

Answer 5

1.) x + y = 141
x + x + 37 = 141
2x = 104
x = 52

52 and 89

2.) x + y = 54
y + 28 + y = 54
2y = 26
y = 13

41 and 13

Answer 6

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