Problems of the Week: February 6 to February 13

Jan 30, 2017 | Lakeland Highlands

stampLower Elementary:
Question: Lucas had 24 stamps. He sent 4 cards with 2 stamps each. How many stamps does Lucas have left?
Answer: 16 stamps
Solution: Lucas uses 2 stamps, 4 times to send the cards. That means he uses 2 × 4 = 8 stamps. So, Lucas has 24 – 8 = 16 stamps left over.


lunchUpper Elementary:
Question: 37.5% of students at Lakeside Elementary School bring their lunch from home instead of buying lunch from the cafeteria. If all of the students at Lakeside Elementary either buy lunch from the cafeteria or bring lunch from home, then what percentage of students at Lakeside Elementary do not bring their lunch from home?
Answer: 62.5%
Solution: The students at Lakeside elementary are split into two “parts” that add together to make the “whole” student body. The “whole” is 100% of the students, and if we subtract the “part” we know from the whole, we can find the “part” we don’t know.

 

100% – 37.5% = 62.5%

 

So, 62.5% of students at Lakeside Elementary buy lunch at the cafeteria.


onionMiddle School:
Question: Jamie has a number of vegetables in a basket. The ratio of onions to tomatoes in the basket is 2:5, and the ratio of tomatoes to carrots in the basket is 4:3. If there are 15 carrots in the basket, then how many onions are there?
Answer: 8onions
Solution: If there are 15 carrots, then there are 20 tomatoes. One way to find this out is to reason that since the ratio of tomatoes to carrots is 4:3 and there are 3 × 5 = 15 carrots, then there must be 4 × 5 = 20 tomatoes.

If there are 20 tomatoes, then there are 8 onions. The ratio of onions to tomatoes is 2:5, and we have to multiply 5 × 4 to get to 20 tomatoes, so there must be 2 × 4 = 8 onions.


controllerAlgebra and Up:
Question: Finley uses 37 arcade tokens to play a racing game 5 times and a puzzle game 3 times. Phoebe uses 18 tokens to play each game twice. How many tokens does it take to play the racing game?
Answer: 5 tokens
Solution: We can solve this problem with a system of equations.

 

5r + 3p = 37
2r + 2p = 18

 

One way to solve this system is to divide each term in the second equation by 2 in order to put it in terms of r, the racing game: p = 9 – r. From there, we can substitute 9 – r into the other equation: 5r + 3(9 – r) = 37. We then find that r = 5.