# Problems of the Week

Mar 23, 2020 | High Park

We hope you're keeping well, Mathletes! We miss seeing you guys at the centre but we'll hopefully get to see you soon online with Mathnasium@home! There's no theme this week, just: MATH! Enjoy!

Lower Elementary:
Question: Start with 1. Add 15. Subtract 11. Double it. Add 1. Multiply by 5. Subtract 30. Take away half. What’s the new number?

Upper Elementary:
Question: It takes Evelyn 8 minutes to jog all the way around a circular path. If Evelyn starts at 6:35 AM and jogs around the path exactly 8 times, what time will it be when she’s done?

Middle School:
Question: 24–karat gold is 100% pure gold. How many ounces of pure gold are there in a 15 pound, 16–karat gold bar?

Algebra and Up:
Question: There are two perpendicular lines graphed on a plane. Line A goes through the points (2, 1) and (6, 3). Line B goes through (2, 1) and (x, 5). Solve for x.

...

Answers:

Lower Elementary:

Question: Start with 1. Add 15. Subtract 11. Double it. Add 1. Multiply by 5. Subtract 30. Take away half. What’s the new number?
Answer: 12½
Solution: After we add 15 to 1, we have 16. Then we subtract 11, so we have 16 – 11 = 5. After we double it, we have 5 × 2 = 10. One more makes 11. Next, we have 11 × 5, which makes 55. Thirty less than 55 is 25. Since 25 is odd, we can find half of it by finding half of 24 and half of 1. Half of 24 is 12, and half of 1 is ½, so that gives us a final answer of 12½.

Upper Elementary:
Question: It takes Evelyn 8 minutes to jog all the way around a circular path. If Evelyn starts at 6:35 AM and jogs around the path exactly 8 times, what time will it be when she’s done?
Answer: 7:39 AM
Solution: Eight minutes, 8 times is 8 × 8 = 64 minutes. There are 60 minutes in an hour, so Evelyn jogs for 1 hour and 4 minutes because 64 minutes – 60 minutes (1 hour) = 4 minutes. One hour after 6:35 AM is 7:35 AM, and 4 minutes after that is 7:39 AM.

Middle School:
Question: 24–karat gold is 100% pure gold. How many ounces of pure gold are there in a 15 pound, 16–karat gold bar?
Answer: 160 ounces
Solution: 16–karat gold is 16/24 pure gold, or 2/3. Since two thirds of the gold bar is pure gold, that means that there are 15 × 2/3 = 10 pounds of pure gold. There are 16 ounce in a pound, so 10 pounds of pure gold is the same as 160 ounces of pure gold.

Algebra and Up:
Question: There are two perpendicular lines graphed on a plane. Line A goes through the points (2, 1) and (6, 3). Line B goes through (2, 1) and (x, 5). Solve for x.
Answer: x = 0
Solution: To solve for x, we need to know the slope of Line B. Line A and Line B are perpendicular, so the slope of Line B is the opposite of the reciprocal of the slope of Line A. Line A’s slope is (y2 – y1) ÷ (x2 – x1) = (3 – 1) ÷ (6 – 2) = 1/2 , so the slope of Line B must be –2. Now that we have a point on the line and its slope, we can write an equation in slope-intercept form:

y = –2x + b
y = 1 x = 2
1 = –4 + b
b = 5
y = –2x + 5

5 is the y–intercept. When y = 5, then x = 0.