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Home Q & A Board Science-Related Homework Help Mathematics
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mikejuies mikejuies
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12 years ago
The sum of 2 numbers is 54 and their difference is 26. What are the numbers?Please show work.
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robjenkensrobjenkens
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#1
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12 years ago
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This verified answer contains over 140 words.
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wrote...
#2
12 years ago
1) x + y = 54
2) x - y = 26

Solve for x in eq.1
x = 54 - y
and sub into eq.2
54 - y  - y = 26
solve eq.2 for  y
54 - 2y = 26
54 = 26 + 2y
54 - 26 = 2y
28 = 2y
28/2 = y
y = 14

Now sub y = 14 into eq.2 to get x
x - 14 = 26
x = 26 + 14
x = 40

Check that x = 40 and y = 14
1) x + y = 54
40 + 14 = 54
YUP
2) x - y = 26
40 - 14 = 26
YUP

Slight Smile
wrote...
#3
12 years ago
You have to make 2 equations, then substitute.

1)    x + y = 54

2)    x - y = 26

From equation 2, x=26+y

Substituting into the first equation,  26+y+y=54

Solving for y, y=14

Then, using one of the other equations, x=40

So the answer is 14 and 40
wrote...
#4
12 years ago
x = first number
y = second number.

     x + y = 54
     x - y = 26  ,   by "Adition method" we obtain:
   ------------------
    2x      = 80

     x       =80/2
     x       = 40.   The first number is 40.

   Doing substitution in any of original equations:
  x + y = 54  so: 40 + y = 54
                                y = 54 - 40 = 14. The second number is 14.

Answers:  The two numbers are 40 and 14.
                                               40 + 14 = 54.
                                               40 -  14 = 26.     !!!!!!!!!!!!


                         
wrote...
#5
12 years ago
x+y=54
x-y=26

To find the value of x, start with an equation. I am choosing the second one because it's easier, but it doesn't matter.

x-y=26               add y to both sides
x=y+26

Then, you substitute the value of x in the other equation.

x+y=54
y+26+y=54          subtract 26 from both sides.
y+y=28                
2y=28
y=14

So, y=14, but now you have to plug the y value into an equation to get the value of x.

x-y=26
x-14=26
x=40

So, x=40 and y=14. Or (40,14)
wrote...
#6
12 years ago
X + y =54

x-y=26

1/2 of 54 is 27

1/2 of 26 is 13

13 and 27=40

x=40, y=14
Proof
x+y (40+14)=54
x-y(40-14)=26
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