Answers to Problems of the Week - June 1 to June 5

Rewards for Problems of the week:

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

Lower Elementary:

Question: Perry has $20.00. He spends $2.75 on breakfast, $10.00 on lunch, and $6.45 on dinner. How much money does he have left?

Answer:  80¢

Solution:  Perry starts with $20.00, then spends $2.75, so he has $20.00 – $2.75 = $17.25 left after breakfast. After lunch, he has $17.25 – $10.00 = $7.25 left. After dinner, he has $7.25 – $6.45 = $0.80, or 80¢.

Upper Elementary:  

Question: Joseph owns and runs a bakery. He makes 10 batches of cookies. Each batch yields 18 cookies. If he sells the cookies in boxes of a dozen, how many boxes can he fill?

Answer:  15 boxes

Solution:   To find the total cookies, multiply the number of batches times the number of cookies per batch. 10 × 18 = 180 cookies. Each box gets a dozen (12) cookies, so we divide 180 cookies by 12 to get the number of boxes. 180 ÷ 12 = 15 boxes of cookies.

 Middle School:

Question: It takes Cameron 2 minutes to make a ham sandwich. It takes Morgan 3 minutes to make a ham sandwich. If they work together, how many ham sandwiches can they make in an hour?

Answer:  50 ham sandwiches

Solution:  If it takes Cameron 2 minutes to make a sandwich, then he can make 60 ÷ 2 = 30 sandwiches in an hour. Morgan takes 3 minutes to make a sandwich, or 60 ÷ 3 = 20 sandwiches. If they work together, they make 30 + 20 = 50 sandwiches in an hour.

 Algebra and Up:

Question: Table A orders two steaks and one salad. Table B orders three steaks and four salads.  If Table A’s bill is $53 and Table B’s bill is $112, what is the cost of one steak and one salad?

Answer:  $33

Solution:  Let’s call the cost of a steak x and the cost of a salad y. We can write the problem as two linear equations. 2x + y = 53 and 3x + 4y = 112. One way to solve this problem is to use substitution. We can rewrite the first equation as y = 53 – 2x and substitute that value of y into the second equation. Solving for x, we have x = 20 So, one steak will cost $20. To find the price for the salad, we substitute the value for x into the first equation. So, one salad will cost $13.

Challenge problem to take home. 10 stars for the correct answer. 

+\red{R}+\yellow{E}?

What is the minimum number of colors required to fill the regions of this graph so that no two adjacent (sharing the same border) regions are the same color?

Answer: 4

Solution: