Meet 4

Mystery

100

In recent elections, 52% of the voters voted for candidate A, and 48% voted for candidate B . If a total of 24,000 voters participated, then this many more voters voted for candidate A.

What is 960 voters Candidate A got 4% more votes. 4% of 24,000 is 960

200

A worm is born 20 millimeters long and grows 10% longer every week. How many millimeters long will it be after eight weeks? Give your question to two decimal places, round to the nearest hundredth.

What is 42.87 Do 20*(110%^8)

300

Every house in a new neighborhood has a water pipe with a diameter of 1 inch as its main water source. If there are 400 houses in the neighborhood, this should be the diameter of the pipe that supplies the whole neighborhood.

What is 20 The water-carrying capacity is proportional to the cross-section of the pipe (the area). The area of a circle is proportional to the square of the diameter, so if we multiply the area by 400, it is equivalent to increasing the diameter by √400 so the big pipe’s diameter should be 20 inches. (This works for radius too)

400

How many integers between 1 and 100 are 5 more than a positive multiple of 6?

What is 15 Do 100-5=95 95/6=15 5r is around 15

500

The temperature at noon is recorded each day for five days in a row. If the temperatures are all different integers and their product is 12, what was the temperature on the warmest day?

What is 3

Geometry

100

The area of a circle is 314 square inches. There are this many inches are there in its circumference. (Use 3.14 for pi)

What is 62.8 The area of a circle is a=r^2*pi, so in our case the radius is r=√(a/pi)=√100=10 inches. The circumference is 2*pi*r=2*3.14*10=62.8

200

A square is inscribed inside a circle with each corner of the square touching the circle. What percentage of the square’s perimeter is the circle’s circumference? Round your answer to the nearest whole percent. Use 3.14 as pi

What is 111%

300

A certain circle has a circumference of 125.6 feet. How many square feet are in the area of the circle? Use 3.14 for pi and round your result to the nearest whole number.

What is 1256

400

Assume that the Earth orbits the Sun along a perfect circular orbit with a radius of 150 million kilometers, and completes the orbit in 365 days and 6 hours. What is the Earth’s average speed around the Sun? Express your answer in Kilometers per Hour (km/hour), rounded to the nearest integer. Use pi = 3.14

What is 107,461/hour

500

A circle has a circumference of 18.84 cm. There are this many square centimeters are in the area of the circle. Round to the nearest hundredth and use 3.14 for pi

What is 28.26?

Number Theory

100

Joe has a loop option on his CD player. When he went to the math meet he put in his favorite 17 track CD. When the meet ended he had finished 57 tracks and was on his 58th. This is the track is he on.

What is the 7th track? The Equation is 58=x(mod17). To find x divide 58 by 17. you get 3 remainder 7.The remainder is x, so x=7.

200

This is the sum of the first 85 numbers in the sequence below 5,11,17,23,29,35

What is 21,845 The common difference is 6, and there are 84 numbers past 5, so first do 5+(84*6) to get the number 509. To get the total of all the numbers add the first and last terms, 514, multiply by the number of terms, 43690, and divide by 2, to get a final answer of 21,845.

300

The Martian day, called a sol, is a little longer than a day on earth at about 24 hours and 40 minutes. There are about 669 sols in one Martian year. If Martians also had a seven day week like ours and little Marty was born on Mars on a Tuesday, what day of the week would it be when Marty celebrates his first birthday? We should assume that Martians celebrate birthdays once per Martian year.

What is Saturday Do Since there are 669 Martian days in a year, there will be 669 ÷ 7 = 95.571428... weeks per year. The decimal part of this number is better understood as 4 extra days beyond the 95 weeks. This means that Marty’s birthday will be four days later in the week. Four days after Tuesday is Saturday.

400

Fiona needed to multiply a number that is two more than a multiple of 7 by some other number, n, to get a number that is three more than a multiple of 7. In other words, she was trying to solve the equation 2n = 3 in Mod 7. What whole number value between 0 and 7 will work for n?

What is 5 Do this to solve the equation 2n = 3 in Mod 7. If we just count by 2’s in Mod 7, we get 2, 4, 6, 1, 3, 5, 0, and then it repeats. It is the fifth multiple of 2 that equals 3 in Mod 7, so the value of n we need is 5. To check this, we calculate 2 * 5 which is normally 10. Subtracting 7 from 10, we confirm that 2 * 5 = 3 in Mod 7.

500

Find the sum of the first 20 terms of the arithmetic sequence below. 35, 47, 59, 71, ...

What is 2980 Do the constant difference between the terms in this arithmetic sequence is 12. By the 20th term, a total of nineteen 12’s will have been added to the 35, which is the first term. Thus the 20th term is 35 + 19 * 12 = 35 + 228 = 263. Now, to find the sum of the terms, we can add the first and last terms, the second and second-to-last terms, etc., to get the same sum ten times. That sum is 35 + 263 = 298, and 10 * 298 = 2980.

Arithmetic

100

What is 135% of 4/9 ? Express your answer as a common fraction in simplest form.

What is 3/5 Do This problem is easier if we convert 135% into the equivalent fraction 27/20. Now we multiply as follows: (27/20)*(4/9)=3/5

200

The store “Mathletes ‘R’ Us” sells sweatshirts with different proofs of the Pythagorean Theorem. The manager purchases the sweatshirts from a distributor at a cost of $12.57 each. She marks up the price so that the price on the tag of each sweatshirt is 60% cost and 40% profit. At the cash register, the customer then has to pay a 5% sales tax on the tag price of the sweatshirt. How much does a customer end up paying for a sweatshirt with a proof of the Pythagorean Theorem? Give your answer in dollars to the nearest hundredth of a dollar.

What is $22.00 Do To mark up the sweatshirt so that the tag price is 60% cost and 40% profit, the manager asks herself the following question: $12.57 is 60% of what number? This corresponds to the equation: 12.57 = 0.6x . The manager has learned to divide by 0.6 to answer the question. This gives a price of $12.57 ¸ 0.6 = $20.95 for the tag price of the shirt. The customer then has to pay a 5% sales tax on this tag price. We can compute the 5% by multiplying $20.95 by 0.05, which is $1.0475 or about $1.05. We then add this tax to the tag price for a total of $20.95 + $1.05 = $22.00. Alternatively, we can find 105% of $20.95 directly by multiplying by 1.05. We get $20.95 ´ 1.05 = $21.9975, which rounds to nearest cent as $22.00.

300

Ron’s grandmother sent him a check for $5000 and told him to deposit it in a money market account that earns interest at an annual rate of 3% and compounds monthly. Ron allowed 4 months to go by before he deposited the check. How much interest income did Ron lose by not depositing the check immediately? Express your result to the nearest hundredth of a dollar. Note: This particular money market keeps track of the nearest millionth of a dollar for purposes of calculating interest owed.

What is $50.19 Do If the annual interest rate of the money market account is 3%, then the monthly interest rate must be 3%÷12=0.25%. After interest is posted at the end of the first month, Ron’s balance would be $5000*1.0025=$5012.50. Then he begins to earn interest on the interest as well as the original money from his grandmother. After the second month, his balance would be $5012.50*1.0025=$5025.03125. After the third month, the balance would be $5037.593828. Finally, after four months, Ron’s balance would be $5050.187813, which rounds to $50.19 to the nearest hundredth of a dollar.

400

Ben The Bold is a visiting dignitary who is entirely unaware of the American custom of tipping waiters and waitresses a minimum of 15% of the cost of the meal. In his country, the standard practice is to leave the equivalent of 8 U.S. dollars, regardless of the cost of the meal. If Ben The Bold leaves an $8 tip for a meal that cost $78.60, how much less than the expected minimum tip did he leave? Express your answer in dollars to the nearest cent.

What is $3.79 Do To calculate 15% of $78.60, we convert the percent to a decimal and then multiply by $78.60. The expected minimum tip is thus 0.15 ´$78.60 = $11.79. Ben The Bold left only $8.00, which is $11.79 – $8.00 = $3.79 less than the expected minimum tip.

500

Jackson invested $5000 in an special account that pays 10% annual interest, compounded annually. What will his account balance be after ten years? Express your answer in dollars to the nearest cent.

What is $12,968.71 Do 5000 (1.1^10)

Algebra

100

Joe and Nick are best friends who live exactly four miles apart. One day, Joe called Nick on the phone and said, “ I've simply got to tell you the rumor I heard as quickly as possible, and I can’t tell you over the phone.” Nick said, “I’ll come right over on my bike.” Joe said, “I’ll start running toward you.” If Joe ran toward Nick at a speed of 6 miles per hour and Nick rode her bicycle toward Joe at a speed of 14 miles per hour, how many minutes later did they meet? Assume that they set out immediately, and express your answer to the nearest whole number of minutes.

What is 12 minutes Do D/(S1*S2) D=distance S1=speed of first guy S2=speed of second dude

200

Daily Double A vendor sells pretzels for $1.25 each and hotdogs for $2.00 each. One day he sold 82 items for a total of $134.75. How many pretzels did he sell?

What is 39 Do If the vendor had sold the pretzels for the same price as the hotdogs, he would have taken in 82*$2.00 = $164. Since the pretzels actually sold for $0.75 less than the hotdog, the difference $164–$134.75=$29.25 can be thought of as the number of pretzels times the $0.75 that he did not take in for each pretzel. Since $29.25 ÷ $0.75 = 39, he must have sold 39 pretzels. Most people would not think so hard about it and would just trust the algebra. Let D be the number of hotdogs and let P be the number of pretzels. We can write the following two equations from the information given: D + P = 82 2D +1.25P =134.75 Doubling the first equation and subtracting the second equation from it, we get: 2D + 2P =164 2D +1.25P =134.75 0.75P = 29.25 Dividing both sides of the last equation by 0.75, we get P = 39.

300

What negative value of x will make the following proportion true? 121/x=x/144

What is –132 Do Cross multiplying, we can turn the proportion into the equation 121×144 = x2. Each of the numbers on the left is a perfect square, so we can rearrange factors without ever multiplying 121 by 144:121×144 =11×11×12 ×12 =11×12 ×11×12 =132 ×132 = x2 The value of x could be positive or negative. The question asks for a negative value that will make the proportion true, so the answer is –132.

400

In parallelogram MATH, MA = 168 mm, AT = 15x + 3 mm, TH = 3xy^3mm,and MH = 108 mm. What is the numerical value of y^x?

What is 128 Do Since opposite sides of a parallelogram have the same length, we can write two equations from the information given: 108 = 15x + 3 and 168 = 3xy^3. Solving the first equation for x, we get 105 = 15x, so x = 105 ÷ 15 = 7. Substituting 7 in place of x in the second equation, we get 168 = 21y^3. This means y^3=168 ¸ 21 = 8, so y = 2. Finally, the numerical value of y^x is 2^7= 128.

500

Together Jim and Bob weigh 357 pounds. Together Jim and Larry weigh 393 pounds. The combined weight of all three men is 565 pounds. How much do Bob and Larry weigh together?

What is 380 Do There are many ways to solve this system of equations. One clever way is to double the combined weight of all three men and subtract the two paired weights. Since Jim is included in both the paired weights, his weight will be subtracted twice and each of Bob’s and Larry’s weights will be subtracted once. This leaves the combined weight of Bob and Larry, which is what we want. Thus, the answer is 2 ´ 565 – 357 – 393 = 1130 – 357 – 393 = 380 pounds. Notice that we did not need to find the individual weights, but, for those interested Larry weighs 208 pounds, Bob weighs 172 pounds, and Jim weighs 185 pounds.