Archived Stumpers (with solutions)
STUMPER #1.17: LOSING YOUR MARBLES
(Did you solve something differently? There's almost always more than one way to solve
a math problem. Sometimes there's even more than one correct solution!)
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1. Marble Pyramid
___You stack magnetic marbles on top of a table into a triangular pyramid like the one below. None of the marbles are blue. There are four marbles along the bottom of each side of the pyramid. Without lifting the pyramid off the table, you spray the sides with blue spray paint. How many marbles have no blue paint on them?
One. (The one that's in the middle of the bottom layer of the pyramid.)
2. Marble Sale
___Sue has ordinary red, yellow, and blue marbles. She has twice as many red marbles as yellow ones. She has two more yellow ones than blue ones. She decides to have a marble sale because she wants to buy one special marble for $3.50. She sells all her marbles for 2 cents each. She earned 84 cents from selling her blue marbles. Did she earn enough altogether to buy the special marble?
She can’t buy the special marble unless she finds herself two more cents. If she sold her blue marbles for 2 cents a marble and got 84 cents, she must have started with 42 of them. She had two more yellow then blue, so she had 44 yellow marbles. She had twice as many red as yellow, so she has 88 red marbles. 88 red + 44 yellow + 42 blue = 174 marbles, so at 2 cents a marble that’s $3.48.