9514 1404 393
Answer:
1. 2x +2y = 310; x -y = 55
2. y = 50, x = 105
Step-by-step explanation:
Let the numbers be represented by x and y. Double the numbers would give 2x and 2y. We're told the sum of the doubled numbers is 310, so one equation is ...
2x + 2y = 310
The difference of the numbers is (x-y). We're told that difference is 55, so the other equation is ...
x - y = 55
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We can divide the first equation by 2, and subtract the second.
1/2(2x +2y) -(x -y) = 1/2(310) -(55)
2y = 100 . . . . . . . simplify
y = 50 . . . . . . . . . divide by 2
x -50 = 55 ⇒ x = 105 . . . . use the second equation to find x
The two numbers are 105 and 55.
