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# Math Problems of the Week - Oct. 9, 2022 to Oct. 15, 2022

Oct 9, 2022 | West Covina

Lower Elementary:

Question: Fennec foxes have huge ears and can hear a grub up to 2 feet underground. Can a fennec fox hear a grub that is 20 inches underground?

Solution: There are 12 inches in a foot. So, 2 feet is 12 + 12 = 24 inches. The grub is 20 inches underground, and since 20 is less than 24 inches, the fennec fox can hear it.

Upper Elementary:

Question: A golden wheel spider tucks its legs in and turns its body into an octagonal wheel in order to travel across the sand. Its legs hit the ground a quarter inch apart. How many times does the spider have to roll over in order to roll a whole yard?

Solution: The wheel spider turns itself into an octagon whose sides are 1/4 of an inch. An octagon has 8 sides, so the perimeter of the wheel spider is effectively 1/4 × 8 = 2 inches. There are 12 inches in a foot and 3 feet in a yard, so there are 12 × 3 = 36 inches in a yard. To roll 36 inches, the spider has to roll over 36 ÷ 2 = 18 times.

Middle School:

Question: A camel can go six months without drinking water. It can also drink water very quickly - 30 gallons in 13 minutes! Find the rate at which a camel drinks in gallons per hour.

Solution: Since the camel drinks 30 gallons in 13 minutes, that means it’s drinking 30/13 (or 24/13) gallons per minute. There are 60 minutes in an hour, so the camel can drink at a rate of 30/13 × 60 = 1800/13 = 1386/13 gallons per hour.

Algebra and Up:

Question:A barrel cactus, a hedgehog cactus, and a saguaro cactus have 1,392 spines altogether. The hedgehog cactus has 144 more spines than the barrel cactus, and the saguaro cactus has 888 more spines than the barrel cactus. How many spines does each cactus have?

Answer: The barrel cactus has 120 spines. The hedgehog cactus has 264 spines. The saguaro cactus has 1,008 spines.

Solution: Based on the information in the problems, we can write a system of 3 equations: B + H + S = 1,392, H = B + 144, and S = B + 888. If we substitute in, the values of H and S that are in terms of B in the second and third equation, we get an equation with only one variable: B + (B + 144) + (B + 888) = 1,392. If we solve for B, then we find that the barrel cactus has 120 spines. From there, we can find that the hedgehog cactus has 120 + 144 = 264 spines, and the saguaro cactus has 120 + 888 = 1,008 spines.

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