PROBLEMS- MATH 208:
1. a group of dogs and ducks have a total of 99 heads and legs, all together. The ducks out number the
dogs 2 to1. How many ducks are there? How many dogs?
Solution: 2*goats = ducks 5*g + 3*d = 99 substitute.
goats = 9 ducks = 18
2. Gary began peeling a pile of 44 potatoes at the rate of 3 per minute. Four minutes later, Christen joined him,
and peeled at the rate of 5 potatoes per minute. When they were finished, how many potatoes had each
peeled?
Solution: 12 + 3x + 5x = 44 where x = minutes.
3. A numismatist decides to divide his coin collection among his children. The oldest gets 1/2 of the collection, the
next gets 1/4, the next gets 1/5, and the youngest gets the remaining 49 coins. How many coins are in the collection?
Solution: 49= x – ( ½ x + ¼ x + 1/5 x ) solve for x (number of coins)
4. Robert took a test of 20 questions. The test was graded by giving 10 points for each correct answer and deducting
5 points for each incorrect answer. Robert answered all 20 questions and received a score of 125. How many wrong
answers did he have?
Solution: He had 5 wrong answers. If he had answered all 20 questions correctly, he would have scored 200.
Since he scored 125, this means he lost 75 points. We must deduct 15 points for each wrong answer; 10 points
that he did not earn for getting it right, plus the 5 points that are deducted for the answer being wrong. 75 lost
points divided by 15 equals 5 wrong answers.
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