The sum of two numbers is 53. three times the smaller number is equal to 19 more than the larger number. what are the numbers?

Let's define some variables first. I'm going to say that x = larger number and y = smaller number. Now let's set up our 2 equations (since we have 2 unknown variables, we need 2 equations to solve for them):

Now, let's solve for x in the first equation, then plug it into the other one to get a tangible value for y:

Now that we know that y = 18, let's plug it back into the first equation to solve for x:

So, x = 35 and y = 18. Therefore, the larger number is equal to 35, and the smaller number is 18

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step-by-step explanation:

answer:   x = 3 + √11     and     x = 3 - √11

step-by-step explanation:

x² - 6x + 9 = 11

(x - 3)² = 11

x - 3 = ±√11

    x = 3 ± √11

x = 3 + √11     and     x = 3 - √11