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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.