Problem of the Week #20: March 10th – March 14th, 2008

Grade 6:
A student had twenty dollars. He went to the movies. He paid $ 8.00 for admission, $4.00 for popcorn and $2.50 for a soda and $1.50 for candy. When he looks at his change he has 8 coins. What coins does he have and how many of each does he have?

Grade 7:
The difference of two perfect square three digits numbers is a perfect square number. What are the two numbers and what is the difference?

Grade 8:
A three digit number ABC is divisible by 7 and the same three digits when arranged in the order CBA is also divisible by 7. Find one possible combination for ABC.

Grade 9:
A right triangle has sides measuring 20 cm, 15 cm and 25 cm. Find the shortest altitude for this triangle.

Grade 10:
I am thinking of a three digit number. If I reverse the digits so that the hundreds digit and the ones digit are reversed I get another three digit number. If a multiple the original number by the reversed number the product is 65 125. What is the smaller three digit number?