New Year, New Problems! Test your brain with these puzzles!

**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?

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**Answers**

**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: *3^{1}/_{3} pounds of 20% cacao chocolate and 6^{2}/_{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 = 3^{1}/_{3}. That means that there are 3^{1}/_{3} pounds of 20% cacao, so there must be 10 – 3^{1}/_{3} = 6^{2}/_{3} pounds of 50% cacao.