Please review the solutions to the previous week's problems. Then, move on to this set.
1. Sally is thinking of a number. The product of the digits is one half of the number. What is the smallest positive, two-digit integer she could be thinking of?
2. Find the hypotenuse of a triangle with legs of length 20 and 21.
3. If the hypotenuse of a right triangle is 25, then what is the smallest possible leg, if the two legs must be whole-integer lengths?
4. If you take Isabella’s age, double it, and add 1, you'll get the 9th prime number. How old is Isabella?
5. Bob the panda eats at a rate of 1 bamboo stick per minute. His friend Alice the panda eats at a rate of 2 bamboo sticks a minute. How long, in hours, would it take for them to finish a pile of 3000 bamboo sticks?
Maya's problem is on the run! Please see the marathon.
ReplyDelete1. 10
ReplyDelete2. 29
3. 5
4. 11 years old
5. 37.5 hours
1. 36
ReplyDelete2. 29 -- Pythagorean theorem
a²+ b²= c² (² = squared)
3. 7 Pythagorean theorem
4. 23 years old
5. 16.6 hours
Sorry, #4- 11 years (i was thinking of the 9th prime number)
ReplyDeleteMaya, check your work for problems 1, 3, and 5. Let me know if you need any hints.
ReplyDeleteAvanthika, good job! Give your answer to problem 5 again, and don't round it unless the problem says to.
You guys are quick to answer! Keep up the good work!
ReplyDelete1. 36
ReplyDelete3. 7
5. 16.64
1) 36
ReplyDelete2) 29
3) 7
4) 11
1) 36
ReplyDelete2) 29
3) 7
4) 11
5) 16.64
You all have done a great job answering this set! I'll post the solutions soon.
ReplyDeleteIn the meantime, please visit the marathon and provide a solution to the current problem.
5) 16.64
ReplyDeleteHow are you guys getting 16.64 as an answer?
ReplyDeleteSolutions
ReplyDelete1. Call the tens digit a and the ones digit b. Then, the numerical value is 10a + b.
Now we know that ab = 1/2 × (10a + b), so 2ab = 10a + b. Hence, b is even. Playing around a bit, we find that the number satisfying these conditions is 36.
2. We use the Pythagorean Theorem.
20² + 21² = 841
√841 = 29
3. This is the commonly known 7-24-25 right triangle. Hence, our smallest leg is 7 units in length.
4. The ninth prime number is 23. Subtracting 1 and dividing by 2, we have 22 ÷ 2 = 11.
5. Bob and Alice eat a total of 3 bamboo sticks per minute. Therefore, it takes 1000 minutes for them to eat the pile of 3000 bamboo sticks.
1000 minutes = 16 2/3 ≈ 16.67 hours
Please work on the marathon problem.
ReplyDelete