Problems of the Week July 11 - 15

Below are this week’s Problems of the Week. Answers are at the end of the post.

Lower Elementary:

Question: Texas became a state in 1845. Twenty-six years later, Dallas legally became a city. How many years has Dallas been a city?

Upper Elementary:

Question: In 2014, the Dallas Cowboys won 3/4 of the football games they played. If they lost 4 games, then how many games did they win?

Middle School:

Question: A Texas Longhorn bull’s horns reach 50% of their full length after a year. A four-year-old Texas Longhorn’s horns are 95% their full length. If a one-year-old Texas Longhorn has horns that are 1’ 8” long, then how long will its horns be 3 years later?

Algebra and Up:

Question: The value of D is greater than 0 but less than 1. Write the following in order from least to greatest: D, D2, and √D.

Warning:  Answers are below!

Lower Elementary Answer: 145

Solution: It’s 2016 right now, so Texas is 2016 – 1845 = 171 years old. Dallas is 26 years younger than Texas, so Dallas has been a city for 171 – 26 = 145 years old.

Upper Elementary Answer: 12 games

Solution: If the Cowboys won 3/4 of their games, then they lost 4/4 – 3/4 = 1/4 of their games. We know that one fourth of the games is 4 games, and they won three fourths of the games, so they won 4 × 3 = 12 games.

Middle School Answer: 38” or 3’ 8”

Solution: First, let’s find out how many inches long the bull’s horns are. One foot is 12 inches, and 12 + 8 = 20 inches. Twenty inches is 50% the full length of the horns, so the full length is 20 × 2 = 40 inches. Now, let’s find 95% of 40: 0.95 × 40 = 38 inches, or 3’ 2”.

Answer: D2 < D < √D Solution: D is a proper fraction. If we square D, it gets smaller because a fraction of a fraction is smaller than the original fraction. So, D2 < D. By the same logic, we know that √D must be greater than D; if multiplying a fraction by itself makes the fraction bigger, then taking the root of the fraction must make it larger. So, D2 < D < √D.