Math Problems of the Week - Jan. 22, 2023 to Jan. 28, 2023

Lower Elementary:

Question: Abigail has 75 cents in coins. She has 1 quarter, 2 dimes, and the rest are nickels. How many nickels does Abigail have?

Answer: 6 nickels

Solution: Since a quarter is worth 25¢ and a dime is worth 10¢, Abigail has 25¢ + 10¢ + 10¢ = 45¢. Since she has 75¢ worth of coins, that means she has 75¢ – 45¢ = 30¢ in nickels. Since a nickel is worth 5¢, Abigail must have 6 nickels in total because it takes 6 nickels to make 30¢.

Upper Elementary:

Question: The Lakeside Elementary School Choir is hosting a fund-raising concert event. They sold child tickets for $10 each and adult tickets for $20 each. They made $2,000. If they sold 60 adult tickets, how many child tickets did they sell?

Answer: 80 child tickets

Solution: The amount of profit they made from selling adult tickets is 60x$20=$1,200. Since they made a total of $2,000, the profit made from selling child tickets is $2,000 - $1,200 = $800. They sold child tickets for $10 each, so the number of child tickets sold was $800 ÷ $10 = 80 tickets.

Middle School:

Question: What number(s) between 250 and 275 is divisible by 2, 3, and 9?

Answer: 252 and 270

Solution: A number that is divisible by 2 is even. Between 250 and 275, the even numbers are 252, 254, 256, 258, 260, 262, 264, 266, 268, 270, 272, and 274. A number that is divisible by 9 is also divisible by 9. There are two numbers whose digits have a sum of a number divisible by 9. There are two numbers whose digits have a sum of a number divisible by 9: 252 and 270.

Algebra and Up:

Question: What is the equation of a line perpendicular to y = –2/3x + 3 and goes through the point (1, 3)? Give your answer in slope-intercept form.

Answer: y = 3/2x + 3/2

Solution: If two lines are perpendicular, that means their slopes are the opposite reciprocal to one another. Since the slope of the given line is –2/3, the slope of the perpendicular line is 3/2. Since the line goes through the point (1, 3), we can plug the points into the slope-intercept form to find that the value of b is 3/2. The equation of the line is therefore y = 3/2x + 3/2.