Math Drills
Various Word Problems Review
A-2Word Problems (Work Rate, etc.)
What this worksheet covers
Grade 6 (Elementary School) / Various Word Problems
Word problems solved by spotting a rule are collected here. Patterns giving the color or the weekday at a given position, the growth of savings, work-rate problems with two people cooperating, problems about Cranes and Turtles, elimination problems that cancel one unknown across two expressions, and age problems each come with their own way of setting up an expression and drawing a diagram.
With patterns, the remainder after dividing by the cycle length gets misread, and a remainder of 0 is answered with the first color. In Cranes and Turtles, the difference produced by assuming everything is a crane is divided by the total count instead of by the difference in legs per animal. In age problems, children cannot make use of the fact that the gap between two ages never changes.
Comparing two people's motion at once, the organizing principle of Traveler Problems, is applied here across a much wider range of settings, from work-rate problems to age problems. Representing an unknown with a box, the method used in Various Word Problems in grade 5, widens into elimination, solving by weighing two expressions against each other. Reasoning that carries on into junior high school and beyond is folded into this unit as well.
- Work-Rate Problems · Two People Working Together1 question
- Work-Rate Problems · The Remaining Work1 question
- Crane and Turtle Problems · Shopping Problems2 questions
- Elimination Problems · Subtracting Directly to Eliminate1 question
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Problems and answers on this worksheet
These are the problems in “Various Word Problems”, shown with their answers.
(1)To assemble a certain bookshelf, person A 1 takes 12 hours, and person B 1 takes 24 hours. If person A and person B do this job, the 2 of them, in how many hours can they finish it? Answer □
Answer: 8hours
(2)To finish organizing books, A 1 person working alone would take 15 days. A works first for 5 days, and then B 1 person finishes the rest alone in 4 days. If B 1 person did the whole job alone, how many days would it take? Answer □
Answer: 6days
(3)You bought 1 for 100 dollars trading cards and 1 for 180 dollars gems for your collection, 9 in total, and the cost was 1300 dollars. How many of each did you buy — trading cards and gems? trading card □ gem □
Answer: 4trading cards, 5gems
(4)You bought 1 for 60 dollars autographed baseballs and 1 for 150 dollars autographed basketballs for your collection, 12 in total, and the cost was 1170 dollars. How many of each did you buy — autographed baseballs and autographed basketballs? autographed baseball □ autographed basketball □
Answer: 7autographed baseballs, 5autographed basketballs
(5)2 wallets and 1 backpack cost 280 dollars, and 2 wallets and 3 backpacks cost 480 dollars. What is the price of 1 wallet and 1 backpack each? 1 wallet □ 1 backpack □
Answer: 90dollars, 100dollars
