Word problems

The roots of $$x^2-6x+10=0$$ are $$x_1$$ and $$x_2$$. Find an equation whose roots are $$\frac{x_1}{x_2}$$ and $$\frac{x_2}{x_1}$$

Find three consecutive odd numbers with a sum of 63

A ball is dropped from a 100 feet building. How far will it have traveled when it hits the ground for the 10th time? The ball loses 25% of its height after each bounce.

Bonny is five years younger than Roger and four times as old as Dana. If Dana is $$d$$ years old, how old is Roger in terms of $$d$$?

If $$b$$ is an integer that satisfies the inequality $$4<\sqrt{b}\le 8$$ , what is the sum of the largest possible value of $$b$$ and the smallest possible value of $$b$$?

$$3$$ bananas and $$8$$ grapes cost $$\$1.91$$. $$14$$ bananas and $$25$$ grapes cost $$\$8.05$$. What is the cost of $$8$$ bananas and $$16$$ grapes?

A certain sample of bacteria triples in number every hour. If there were $$8$$ bacteria in the sample at the start of the experiment, how many bacteria were there after $$6$$ hours?

When four times the difference of a number $$n$$ and fifteen is divided by three, the result is twelve. What is the value of $$n$$?

A basketball team won $$11$$ more games than it lost. If the team played a total of $$81$$ games and there were no ties, how many games did the team lose?

If the remainder is $$5$$ when a positive integer $$b$$ is divided by 7, then what is the remainder when $$9b$$ is divided by $$7$$?