# algebra

The sum of a number and three times another number is 18. Find the number if their product is a maximum.

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1. x + 3y = 18
z = xy = (18-3y)(y) = 18y-3y^2
This is just a parabola with vertex (maximum value) at y=3

so, x=9, y=3

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2. thirty times a number less three

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3. the difference between eight and thrice a number plus eight

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4. five less than a number is fifty

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5. half a number decreased by ten

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6. if the number is tripled,the result will be the same as when 28 is added to the number.What is the number

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7. thirty times a number less three
30n-3

the difference between eight and thrice a number plus eight
8-3n+18

five less than a number is fifty
5-n=15

half a number decreased by ten
1/2n-10

if the number is tripled,the result will be the same as when 28 is added to the number.What is the number?
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54
KnowMyPain

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255.9K people helped

Let the number be x

According to question.

3x = x+28

2x = 28

x = 14.

The number is 14.

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