Snowman Geometry

For the following problems, assume that the snowballs are perfect spheres.

Chiquita and Rhonda are each building a snowman. Rhonda tells Chiquita that she is making each of her 3 balls of snow 20% smaller than the one below it. Rhonda starts by making the base ball with a diameter of 20 inches. If she reduces the diameter by 20% each time she makes a new ball, what is the diameter of the third ball she makes (the ball for the snowman’s head)? Express your answer as a decimal to the nearest tenth.

 

Fall vs. Autumn

As the weather is turning cooler and daylight is arriving later in the morning and trees are starting to lose their leaves, many of us are noticing that summer is over and we’re well into fall.  Or is it autumn?  Mr. Kravis surveyed his class, and out of 28 students (with every student picking exactly one of the two options), the ratio of the number of students who called the season “fall” to the number of students who called the season “autumn” was 3:1.  How many students called the season “fall?”

Flu Shot Frenzy

Some organizations are looking to make a lot of money off of the flu vaccine that is in such high demand.  A survey done last week reported that 55% of 677 hospital pharmacists who responded reported being offered the vaccine at highly inflated prices.  Of those, 84% said they would not buy the vaccine at those prices.  How many of the 677 hospital pharmacists did not say that they would not buy the vaccine at the high prices?  Express your answer to the nearest whole number.

Field Trips

The ratio of girls to boys in Mrs. Franks’ 7th grade class is ¾ (excluding Mrs. Franks). On Monday, 4 girls and 6 boys got to go on a special field trip for honor roll students. Since no other students were absent on Monday, the ratio of girls remaining in the class to boys remaining in the class was 4/5. How many students are in Mrs. Franks’ class when everyone is present?

American Idol Mania!

Season 17 of American Idol ended earlier this year. At the end of the season finale, each of the three judges was asked to share his/her opinion about who should win the contest; Laine or Alejandro.  Each of the three judges responded and audiences around the country basically heard “Laine,” “Laine,” “Laine.”  If each judge answered either “Laine” or “Alejandro,” how many additional ways could the judges’ responses have been heard? 

Getting Ready for School

It’s probably a little strange to think that some students started school last week, some have another couple of weeks of summer vacation and still others are just continuing with their year-round school schedule!  The date of the beginning of the school year has been a topic of debate throughout the last decade (and even before) in many areas across the United States.  But the trend is definitely leaning towards starting school earlier rather than later.  Basically, in the last 10 years, the percent of public schools going back to school before Labor Day has increased by 63%

End of Summer Pool Party

A town in South Dakota decides to have an “End of the Summer” pool party and invites all of the households in the town that have school aged children.

 

Twenty-seven households are invited to the party and the ratio of 5-person households to 4‑person households to 3-person households to 2-person households invited is 1:4:3:1, respectively. (The invite list did not include households of any other sizes.)  How many people from households with less than 4 people are invited to the party?

Summer Jobs

This summer Owen and Jack will both have part time jobs. Owen will be working as a lifeguard and Jack will be working as a server at a local restaurant. Owen plans to work 15 hours each week and will be making $7 per hour. Jack will make an hourly rate of $2.10 plus 18% of his sales in tips. If Jack averages $30 in sales per hour, how many hours will he need to work in order to make the same amount per week as Owen?

The Day That Goes on Forever

March 14 has been dubbed Pi Day.  That’s because March 14 is often written 3/14, and a decimal approximation of pi is 3.14.  But that’s only if you use decimals and our style of writing dates.  In some countries, it’s customary to list the date first followed by the month; for example, March 14 would be 14-3 in some places.  Consequently, some places celebrate Pi Approximation Day on July 22, because that date can be written as 22-7, and a fractional approximation of pi is 22/7. What percentage of the year occurs between Pi Day and Pi Approximation Day?