Some years back, a budget of $25,000 was available to construct 5000 feet of curbing along the road entering Olympic state park. It was desirable to have the maximum possible amount of the more attractive rock curbing and to have the remainder be asphalt diking. At that time, rock curbing cost $6.15 per linear foot and asphalt diking cost $4.30 per linear foot. How much rock curbing could be installed? (Round answer to the nearest foot.)
Set 15
Batting Average Raising
A baseball player has been officially at bat 322 times and has a batting average of 0.289 (the number of hits divided by 322 is 0.289). He figures that he will have 53 times at bat for the rest of the season. What batting average does he have to maintain for the rest of the season so that he will end the season with a batting average of at least .300?
Square of Smaller Plus Larger
Take two numbers whose sum is 1. Which do you think is larger: the square of the smaller added to the larger or the square of the larger added to the smaller? Why?
Difference of Squares 1
Find the difference between 142 and 132. What’s the difference between 1812 and 1802? Write a formula for the difference of the squares of two consecutive integers, in terms of the smaller of the two. What can you say about the number you get each time?
Consecutive Integers, Sum of 17802
Find four consecutive integers whose sum is 17802.
Boys, Girls, Bikes
Three students are named Sean, Juan, and Tran Vo. Each owns one of the following bicycles: a Trek, a Gary Fisher, and a Surly. Each student also has a girlfriend. The girls’ names are Carmen, Monique, and Beth.
Tran Vo neither owns a Surly nor is Monique’s boyfriend. The Trek does not belong to Juan nor is Carmen his girlfriend. If Carmen’s boyfriend is either Juan or Tran Vo, then the Surly belongs to Beth’s boyfriend. If the Surly belongs to Juan, then the Gary Fisher does not belong to Carmen’s boyfriend. What is the brand of each student’s bike and his girlfriend?
Slow Watch
My watch says 1:30 (p.m.) My watch is 20 minutes slow, and it is losing 10 minutes an hour after a bus ran over it last week. I have got to be in a phone booth at 6th Avenue and 44th Street at exactly 4:00 to receive my next instructions. If I don’t reset my watch between now and then, at what time by my watch should I step into the phone booth?
Dimes and Pennies (2 Equations)
You have been saving dimes and pennies in a jar on your dresser. One day you dump them out. There are 181 coins and you have $10.54 total. How many dimes do you have?
Crypt-Prod: As a Man
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In the product at the left, each different letter stands for a different digit. What digit does A stand for?
L-Block, Section
Consider this L-shaped block. What is the maximum total number of the faces of the pieces produced by one plane cut through the block?