## Quantitative Reasoning

## Defined Operations 2; Do Composition

If 3 *h* = 10, 7 *h* = 50, 5 *h* = 26; and 4 *b* = 1, 7 *b* = 2.5, 20 *b* = 9, then what is *n*

if *n hb* = 17.5?

## Defined Operations 3; Do Composition

If 10 *g* = 16, 100 *g* = 196, 4 *g* = 4 and 12 *r* = 5; 300 *r* = 101, 30 *r* = 11, then what is *n* if *n* *g* *r* = 9?

## Newton’s Cows

This problem has been attributed to Sir Isaac Newton. Three cows eat in two weeks all the grass on two acres of land, together with all the grass that grows there in the two weeks. Two cows eat in four weeks all the grass on two acres of land, together with all the grass that grows there in the four weeks. How many cows, then, will eat in six weeks all the grass on six acres of land together with all the grass that grows there in the six weeks? Assume that the quantity of grass on each acre is the same when the cows begin to graze, that the rate of growth is uniform during the time of grazing, and that the cows eat the same amount of grass each week.

## Okla Homer Baggage

When Homer Smith and his wife Okla flew to Rome, they had together 94 pounds of baggage. Homer paid $15.00 and Okla paid $20.00 for the excess weight of their baggage. If Homer had made the trip by himself with the combined baggage of both of them, he would have had to pay $135.00 for excess baggage. How many pounds of baggage can one person take along without charge?

## Defined Operations 1

Define an operation $ for positive real numbers so that *a* $ *b = ab*/(*a* + *b*).

Then 4 $ (4 $ 4) = what?

## Defined Operations 2

If a v b means ab + 1 and a @ b means a + b, then evaluate

## Defined Operation 2; 5 Parts

The operation *x*,*y* is defined by *x*,*y* = (*x* + 1)(*y* + 1) – 1 = *xy* + *x* + *y*. Which of these statements is false?

*x*,*y*=*y*,*x*for all real*x*and*y*.*x*,(*y*+*z*) = (*x*,*y*) + (*x*,*z*) for all real*x*,*y*, and*z*.- (
*x*– 1),(*x*+ 1) = (*x*,*x*) – 1 for all real*x*and*y*. *x*,0 =*x*for all real*x*.*x*,(*y*,*z*) = (*x*,*y*),*z*for all real*x*,*y*, and*z*.

## Defined Operation; Find Formula

If 4 → 3, 10 → 6, 7 → 4.5, then what is the formula for *x* → ?

## Defined Operation; Do Inverse

Suppose a linear operation �/� is defined so that:

5 / = 11;

8 / = 17;

12 / = 25.

What is *n* if *n* / = 35?