If a hen and a half lay an egg and a half in a day and a half, how long will it take ten hens to lay ten eggs?

## Set 02

## Farmers’ Market, Chickens, Geese

At the Farmer’s Meat Market, Theo will sell you a certain number of geese for $27. Four more chickens than that cost $42. Six chickens and two geese will cost you $45. How much would you have to pay for one chicken? How much for one goose?

## Inequality with Fractions

## Inequality as Distance

The locus of points *P* on the number line such that the distance between *P* and the point 2 is between 1 and 7 inclusive, is:

*P*≤ 1 or*P*≥ 3- 1 ≤
*P*≤ 3 - -5 ≤
*P*≤ 9 - -5 ≤
*P*≤ 1 or 3 ≤*P*≤ 9 - -6 ≤
*P*≤ 1 or 3 ≤*P*≤ 10

## Radical Has Real Values

For how many real numbers *x* is a real number?

- none
- one
- two
- a finite number greater than two
- infinitely many.

## Maximize Fraction, Bank Robber

You have just caught a bank robber and are about to collect a reward. The reward will be given to you according to this formula: Reward = and you can pick the values of *x* and *y* as follows:

*x*= -7, -2, 0, or 10;

*y*= -3, -2, 1, or 20.

Which values should you pick so that you maximize your reward?

## Difference of Reciprocals

## Tree and Pole

How tall is a tree that is 25 feet shorter than a telephone pole that is three times as tall as the tree?

## The Scale

As soon as wrestling practice was over, Augie jumped on the scale to see how his weight was doing. But Benny jumped on with him, so Augie couldn’t tell how much he weighed. All the boys could see was that their combined weight was 201 pounds. Then Benny pushed Augie off the scale so he could see about his own weight, but Chuckie jumped on next to Benny. The combined weight of those two was 226 pounds. Then Chuckie pushed Benny off, but Augie still wanted another try, so he jumped on with Chuckie. Their combined weight was 219 pounds. Then the coach chased them away from the scale. The boys remembered those three numbers, though, and they were able to figure out their individual weights. Can you do it too?

## Toy Rocket

A toy rocket is lying on its side, ready to be raised into position on its launch pad in the middle of Tappan Square. Stage C (the top stage of the three stages) is 22 cm long. Stage B is as long as Stage C plus 1/2 of stage A. Stage A is as long as stage B and stage C together. How tall is the whole rocket?