SOLUTION: I need help with this if someone could. A positive integer is 33 more than 24 times another. Their product is 9291. Find the two integers.

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Question 1170839: I need help with this if someone could.
A positive integer is 33 more than 24 times another. Their product is 9291. Find the two integers.
Found 2 solutions by Alan3354, Theo:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A positive integer is 33 more than 24 times another. Their product is 9291. Find the two integers.
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Find a pair of factors of 9291 that fit.
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If you know about the quadratic equation, use that.
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You learn nothing by having someone do it for you.

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
let a be one of the integers.
let b be 33 more than 24 time the other.

your 2 equations are:

a * b = 9291.

a = 24 * b + 33

replace a with 24 * b + 33 in the first equation to get:

(24 * b + 33) * b = 9291

simplify to get:

24 * b^2 + 33 * b = 9291

subtract 9291 from both sides of the equation to get:

24 * b^2 + 33 * b - 9291 = 0

factor this quadratic equation to get:

b = -20.375 or 19.

b has to be an integer and has to be positive, so the answer is most likely b = 19.

replace b in the equation of a * b = 9291 to get:

a * 19 = 9291.

solve for a to get:

a = 9291/19 = 489.

replace a with 489 and b with 19 in the equation of a = 24 * b + 33 to get:
a = 24 * 19 + 33 = 489

both equations are satisfied when a = 489 and b = 19.

your solution is that the two integers are 489 and 19.