Math Problems of the Week - Feb. 12, 2023 to Feb. 18, 2023

Lower 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 2x4=8 stamps. So, Lucas has 24-8=16 stamps left over.

Upper 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 at 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.

Middle 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: 8 onions

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 carrots is 4:3 and there are 3x5-15 carrots, then there must be 4x5=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 5x4 to get to 20 tomatoes, so there must be 2x4=8 oions.

Algebra 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.