Answers to Problems of the Week - November 8 to November 14

Rewards for Problems of the week:

5 stars for the correct answer at your level; 10 stars for the next level; 20 stars for 2+ levels up.

 Lower Elementary:

 Question: Abigail has 75¢ 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 60 × $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 3, so we only have to check divisibility by 9. A number is divisible by 9 if the sum of the digits is 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.

Challenge problem to take home. 5 stars for the correct answer. 

What is the least number of guards needed to completely guard this art gallery?

The guards cannot move, and every part of the gallery must be in the line of sight of at least one guard.

Answer: