As for the second equation, you can assume either variable to be the smaller without loss of generality, so let's say that the smaller one is simply for the sake of the tidiness of alphabetical order. The difference of the two is then and 26 more than the smaller must be , hence:
An equation that you will want to put into standard form so that you can solve the system by elimination, so:
John
My calculator said it, I believe it, that settles it
You can put this solution on YOUR website! Q:The sum of two numbers is 38 and their difference is 26 more than the smaller one. What are the two numbers?
A: You will want to translate the english version of this problem into algebra. Start with the first part of the first sentence: The sum of two numbers is 38.
We know that SUM is ADDITION, so this meas two numbers added together equal (IS) 38. So if the smaller number is x and the larger is y, then
x + y = 38.
Now, the second part of the sentence, their difference is 26 more than the smaller one. The DIFFERENCE means subtraction. We subtract the two unknowns, y - x since x was the smaller. This is equal to 26 more than the smaller. MORE THAN means addition (x + 26). So now we can build a second equation,
y - x = x + 26.
Depending on what level of mathematics you are in you can solve using two variables or substituting 38-x for y in the second equation and then using just one equation and one variable.
x + y = 38 & y - x = x + 26:list both equations
y = 38 - x & y = 2x + 26: solve for y
38 - x = 2x + 26:substitute for y since both equations are equal to y
12 = 3x: subtract 26 from both sides and add x to both sides
4 = x:divide by 3
y = 38 - x :go back to your first equation
y = 38 - 4 :substitute x=4
y = 34 :subtracct
Double check: y - x = x + 26
y = 34, x = 4
34 - 4 ?=? 4 + 26
30 = 30
So the correct solution are the numbers 4 and 34 just as you had found.
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