# Proportional Reasoning

## 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?

## Shaping Up

Jayden started a new exercise program that includes running, cycling, yoga and aerobics. The chart shows how many calories Jayden burns by doing these exercises. Use this data to answer the questions that follow.

## Happy Halloween

Mrs. Miller bought a half bushel of apples, 16 of which were set aside to be used for apple bobbing at the harvest festival. That left only two-thirds of the apples Mrs. Miller bought. She then used three-fourths of the remaining apples to make four apple pies. If Mrs. Miller was left with just enough apples to make two caramel apples for each of her children, how many children does Mrs. Miller have?

## Fall Leaves

It’s Autumn, and that means leaves are falling! Amber’s house occupies 2650 ft^{2} in the middle of a 50-foot by 80-foot parcel of land, and the leaves that fall cover the ground all around her house. If it takes Amber’s family 4.5 hours to rake all the leaves, how many square feet of leaves did they rake each hour?

## Columbus Day

Christopher Columbus landed in the Americas accidentally. He was actually trying to find a faster trade route to Asia from Spain. Instead of sailing around the tip of Africa, Columbus believed he could sail west across the Atlantic Ocean to reach Asia. In planning his expedition, Columbus calculated the journey would be around 2300 miles, based on his estimation of the earth’s size. Nautical experts of the time disagreed with his calculations, estimating the distance would be closer to 12,200 miles.

## Gourmet Candies

Sugar Shack gourmet candy shop’s signature candy mixture contains Sour Drops, Chocolate Chews and Tangy Twists in the ratio 2:3:4, respectively. How many more pounds of Tangy Twists than Sour Drops are in a 45-pound batch of this signature candy mixture?

## Road Work Ahead

A construction crew places orange barrels on both sides of a particular road to indicate a work zone. On each side of the road, the distance between the centers of consecutive barrels is 15 feet. If this work zone is 1.5 miles long, what is the total number of barrels that will be used?

## Summer Funds

Fiona has two part-time jobs during her summer vacation. She works part-time as a counselor at a local day camp, and she has another part-time job as a life-guard at the community swimming pool. Fiona works a combined total of 40 hours every week between the two jobs.

The first week working both jobs it rained all but one day, so three-fourths of the hours she worked that week were at the day camp. How many hours did Fiona work at the pool the first week?

## Archer's Three Sons

Archer has three sons named Tanner, Carver and Decker. Archer’s age is three times the sum of Carver’s and Decker’s ages. The sum of Tanner’s and Carver’s ages is half Archer’s age. If Tanner’s age is three times Carver’s age, what is the ratio of the ages of Carver and Decker? Express your answer as a common fraction.

## Final Countdown

On Sunday, May 13th, 224 middle-school math students participated in the written rounds of the 2018 Raytheon MATHCOUNTS National Competition. On Monday, May 14th, the top 12 competitors will go head to head in the National Countdown Round to determine the 2018 MATHCOUNTS National Champion. Let’s solve a few problems from the 2017 National Countdown Round.