Problem of the Week #15: Posted January 13, 2008

Grade 6
A farmer was selling his produce at the market. He had 50 small baskets with 3 tomatoes in each basket. By the end of the first day he had sold half of his tomatoes. If he sold 7 baskets of tomatoes the following day, how many tomatoes would he have left?

Grade 7
Find a number such that when added to the numerator and denominator of 2/11, the resulting fraction is equivalent to 1/2.

Grade 8
The number 75 can be expressed as the sum of consecutive whole numbers. For example, 13 + 14 + 15 + 16 + 17 = 75 and 10 + 11 + 12 + 13 + 14 + 15 = 75. Find one other set of consecutive whole numbers that sum to seventy-five.

Grade 9
Tom and Rachel each have a collection of coins consisting only of pennies, nickels, dimes, and quarters. Both collections have the same cash value, but they have different numbers of each type of coin. In particular, Rachel has four more quarters than does Tom, but Tom has more of every other type of coin. In fact, Tom has a total of 32 more coins than does Rachel. If Rachel has 23 nickels, how many nickels does Tom have?

Grade 10
A circle is circumscribed around both a square of area 5 and a rectangle of area 4. Find the dimensions of the rectangle.