Question: How much do two pumpkins that each weigh 10-and-a-half pounds weigh together?
Answer: 21 pounds
Solution: Let’s add the whole pounds first, then the half pounds: 10 pounds + 10 pounds = 20 pounds. A half pound plus a half pound makes a whole pound. So, in total, the two pumpkins weigh 20 pounds + 1 pound = 21 pounds.
Question: Mrs. Olson buys one bag of 120 lollipops for $9.60 and a bag of 140 chocolates for $9.80. Which kind of candy is worth more per piece?
Answer: Lollipops
Solution: We can find the cost of each by dividing the value of the bag in cents by the number of candies inside. The lollipops cost 960¢ ÷ 120 = 8¢ each. The chocolates cost 980¢ ÷ 140 = 7¢ each. So, the lollipops are worth more per piece.
Question: Tommy, Masyn, Ray, and Deb are dressed up as a mummy, a ghost, a monster, and a robot to go trick-or-treating, but you can’t tell who’s who! The mummy is too tall to be Masyn or Ray, and the ghost is too short to be Tommy or Deb. The mummy and the ghost are wearing matching shoes that belong to Masyn and Deb. The Monster has freckles, but Tommy does not. Who is in the robot costume?
Answer: Tommy
Solution: One way to solve this is with a table like the one below, eliminating impossible options with each clue.
| Mummy | Ghost | Monster | Robot | |
|
Tommy |
3 | 2 | 4 | |
| Masyn | 1 | 3 | 3 | |
| Ray | 1 | 3 | 4 | |
| Deb | 2 | 3 | 3 |
The numbers in the table represent the order in which each option is made impossible.
Question: A fog machine makes fog out of a liquid mixture that must be one-third fog concentrate and two-thirds water. Right now, there is one cup of fog concentrate and 3 cups of water in the fog machine tank. How much fog concentrate and how much water must be added to fill the 15-cup fog machine tank with a mixture that is one-third fog concentrate? Write an algebraic equation to help you solve the problem.
Answer: 4 cups of fog concentrate and 7 cups of water
Solution: One fourth of the 4 cups in the mixture in the tank is concentrate, so the concentration is 1/4. We must add 11 cups with an unknown concentration to make 15 cups with a concentration of 1/3. As an equation:
4 cups × 1/4 + 11 cups × x = 15 cups × 1/3
We find that x = 4/11. So, 4 of the 11 cups must be concentrate and the other 7 must be water.
