POW April 3rd

Problems of the Week for April 3rd: Answers and Solutions at the bottom.

Lower Elementary:

Question: Brooklyn has 154 blocks and Victoria has 342. They combine their blocks to build a castle, and they use all but 12 of them. How many blocks did Brooklyn and Victoria use on the castle?

Upper Elementary:

Question: Eli picks up 288 seashells at the beach. He divides them evenly among 12 boxes. Then, he gives 7 boxes of seashells to Lincoln. How many seashells does Lincoln get?

Middle School:

Question: A sheet cake is 12 inches wide, 18 inches long, and 4 inches deep. Layla cuts a 4-inch by 4-inch slice of cake from the corner. How many cubic inches of cake are left?

Algebra and Up:

Question: A chocolatier receives an order for a 10-pound chocolate statue whose cacao content is exactly 40%. The chocolatier has 20% cacao chocolate and 50% cacao chocolate at his disposal. How many pounds of each does he need to melt together to have exactly the right amount for the statue?

Lower Elementary:

Question: Brooklyn has 154 blocks and Victoria has 342. They combine their blocks to build a castle, and they use all but 12 of them. How many blocks did Brooklyn and Victoria use on the castle?

Answer: 484 blocks

Solution: First, we add up all the blocks: 154 + 342 = 496. Next, we subtract the blocks that Brooklyn and Victoria didn’t use: 496 – 12 = 484.

Upper Elementary:

Question: Eli picks up 288 seashells at the beach. He divides them evenly among 12 boxes. Then, he gives 7 boxes of seashells to Lincoln. How many seashells does Lincoln get?

Answer: 168 seashells

Solution: When Eli divides the 288 seashells into 12 boxes, he puts 288 ÷ 12 = 24 seashells in each box. Since Lincoln gets 7 boxes, he gets 24 × 7 = 168 seashells.

Middle School:

Question: A sheet cake is 12 inches wide, 18 inches long, and 4 inches deep. Layla cuts a 4-inch by 4-inch slice of cake from the corner. How many cubic inches of cake are left?

Answer: 800 cubic inches

Solution: The volume of the whole cake is 12 × 18 × 4 = 864 cubic inches. The volume of the slice Layla takes is 4 × 4 × 4 = 64 cubic inches. So, the remaining cake is 864 – 64 = 800 cubic inches in volume.

Algebra and Up:

Question: A chocolatier receives an order for a 10-pound chocolate statue whose cacao content is exactly 40%. The chocolatier has 20% cacao chocolate and 50% cacao chocolate at his disposal. How many pounds of each does he need to melt together to have exactly the right amount for the statue?

Answer: 31/3 pounds of 20% cacao chocolate and 62/3 pounds of 50% cacao chocolate

Solution: 40% of 10 pounds of chocolate is 4 pounds, so we know that the total amount of cacao in the mixture must be 4 pounds. We can set up an equation to solve for x, the amount of 20% cacao chocolate:

0.20x + 0.50(10 – x) = 4

Notice that the amount of 50% cacao chocolate is 10 – x. This is because every part of the 10 pounds of chocolate that isn’t the 20% cacao is the 50% cacao. When we solve for x, we find that x = 31/3. That means that there are 31/3 pounds of 20% cacao, so there must be 10 – 31/3 = 62/3 pounds of 50% cacao.