Math Drills
Various Word Problems Review
A-5Word 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 organize a certain shelf, person A 1 takes 12 hours, and person B 1 takes 12 hours. If person A and person B do this job, the 2 of them, in how many hours can they finish it? Answer □
Answer: 6hours
(2)To finish tending a flower bed, A 1 person working alone would take 10 days. A works first for 4 days, and then B 1 person finishes the rest alone in 3 days. If B 1 person did the whole job alone, how many days would it take? Answer □
Answer: 5days
(3)The school bought 1 for 90 dollars backpacks and 1 for 200 dollars books for the new students, 7 in total, and the cost was 960 dollars. How many of each did the school buy — backpacks and books? backpack □ book □
Answer: 4backpacks, 3books
(4)You bought 1 for 10 dollars origami sheets and 1 for 25 dollars rare stickers for your collection, 20 in total, and the cost was 320 dollars. How many of each did you buy — origami sheets and rare stickers? origami sheet □ rare sticker □
Answer: 12origami sheets, 8rare stickers
(5)3 pairs of shoes and 2 basketballs cost 590 dollars, and 3 pairs of shoes and 5 basketballs cost 800 dollars. What is the price of 1 pair of shoes and 1 basketball each? 1 pair of shoes □ 1 basketball □
Answer: 150dollars, 70dollars
