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?
Number Sense and Logical Reasoning
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
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?
Kumquat House Numbers
A new housing development, Mango Manors, is being built outside of town. It costs five cents to buy a single digit house number, but two digits can be bought for nine cents. If each home owner on Kumquat Street, a street with only single digit and 2-digit house numbers, buys the numbers for his own house, the total amount paid is $2.15. If one person buys them all, then the total amount paid is $2.12. How many single digit house numbers are on Kumquat Street?
- 3
- 4
- 5
- 6
- 7
Supermarket, Apples
The Superduper Supermarket has 128 crates of apples that have just arrived at the loading dock. Each crate contains at least 120 apples and at most 144 apples. What is the largest integer n you can find such that there must be at least n crates containing the same number of apples? (This means that, even if you make the number of apples in each crate as different as you can possibly make them, there are still going to be n crates with the same number of apples.)
- 4
- 5
- 6
- 24
- 25
Kite Strings
Buzz has three kite strings averaging 6600 feet in length. None is less than 6200 feet long. How long can the longest be?
Garden Crops
A large organic nursery has somewhere between 3 and 6 (inclusive) garden plots of herbs when it closes for the season in the fall. In each plot there are between 20 and 30 (inclusive) rosemary plants. If, typically, 10% of those plants don’t winter over successfully until spring, what would be the largest number of plants that could be lost during the winter?