Algebraic Expressions & Equations
Happy New Year! Now that 2019 is here, let’s have some fun solving this collection of problems that all involve the number 2019.
What is the greatest prime factor of 2019?
The factors of 2019 are 1, 3, 673, 2019. The prime factors of 2019 are 3 and 673, the greatest being 673.
As 2018 comes to an end, let’s go back and solve some of our favorite problems of year.
Problem 237: Kendra starts at a positive integer k and counts up by 4s until she hits exactly 200. Mason starts at a positive integer m and counts up by 6s until he hits exactly 200. If it takes Kendra half as many steps to reach 200 as it takes Mason, what is the greatest possible value of k − m?
The Land O’ Lakes High School auditorium has exactly 26 rows of seats. The rows are labeled, in order, from the front of the auditorium to the back from A through Z. There are 8 seats in the row A. Each row after the first row has two more seats than the previous row. There are 10 seats in row B, 12 seats in row C and so on. How many seats are there in row Z?
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?
Margo has some coins consisting of only pennies and nickels. These coins have a combined weight of 1500 g that is evenly distributed between the two types of coins. If each penny weighs 2.5 g and each nickel weighs 5 g, what is the total value of Margo’s coins?
Ms. Cross leads The National Math Club at the middle school where she teaches. At the first club meeting of the school year, 60% of the students in attendance were boys. If there was one fewer girl than boy in attendance, how many students attended the first club meeting?
International Left Handers Day is celebrated each year in August. If the ratio of the number of days of the month before International Left Handers Day to the number of days of the month after it is 2:3, on what date in August is this special day observed?
What is the 20th term of the arithmetic sequence 13, 19, 25, 31, ...?
The common difference is 19 – 13 = 6. Now that we know that we can find the 20th term by 13 + 6(20 – 1). Thus, the 20th term is 127.
What is the sum of A and B in the arithmetic sequence 7, 15, 23, A, 39, B, ...?
Summer Fun Camp enrollment costs 85 dollars each week per camper. Each camper may register for up to three of the optional workshops offered for an additional charge of $5.50 a week per workshop, or 15 dollars per week for three workshops. The total charge for Chloe’s enrollment to attend Summer Fun Camp for n weeks this summer is 768 dollars. If Chloe has registered to participate in two workshops each week, what is the value of n?
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?