SOLUTION: Bob has more money saved than Susan. If they both triple the amount of their savings, which property of real numbers demonstrates that Bob will still have more money than Susan?

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Question 1011427: Bob has more money saved than Susan. If they both triple the amount of their savings, which property of real numbers demonstrates that Bob will still have more money than Susan?
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
B = amount of money Bob has saved up
S = amount of money Susan has saved up

"Bob has more money saved than Susan" means we have this inequality

Multiply both sides by 3 to get . Notice how the inequality sign did NOT flip. This only happens if we multiply both sides by a negative number.

Since , we know that Bob still has more money saved up.

The property being used here is the Multiplication Property of Inequality (since we multiplied both sides of the inequality by 3. The inequality sign will NOT flip since 3 is positive)

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Alternative Method:

The inequality is equivalent to this equation where k is some positive number. For instance, if Susan had 10 dollars and we add on 3 dollars, then Bob has 13 dollars. For this example, S = 10, k = 3 and B = 13

Multiply both sides by 3. I'm using the Multiplicative Property of Equality

Distribution Property

Let

Convert back to inequality form

So if , then just like shown above in the previous method. This alternative method essentially backs up the Multiplication Property of Inequality and shows how it's very similar to the Multiplication Property of Equality.

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Which ever way you think about the inequality, we know that if Bob has more money, and they each triple their savings, then Bob will still have more money.