Math Drills
Various Word Problems Review
A-4Word 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 put up the wallpaper on the wall of a certain storeroom, person A 1 takes 8 days, person B 1 takes 12 days, and person C 1 takes 24 days. If person A, person B, and person C do this job, the 3 of them, in how many days can they finish it? Answer □
Answer: 4days
(2)To finish cleaning a room, A 1 person working alone would take 8 days. A works first for 2 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: 4days
(3)A gift-wrapping shop ordered 1 for 60 dollars rolls of ribbon and 1 for 110 dollars rolls of tape, 17 in total, and the cost was 1270 dollars. How many of each did the shop order — rolls of ribbon and rolls of tape? roll of ribbon □ roll of tape □
Answer: 12rolls of ribbon, 5rolls of tape
(4)The school bought 1 for 130 dollars books and 1 for 180 dollars trumpets for the new term, 7 in total, and the cost was 1060 dollars. How many of each did the school buy — books and trumpets? book □ trumpet □
Answer: 4books, 3trumpets
(5)4 red toy cars and 3 blue toy cars cost 360 dollars, and 4 red toy cars and 5 blue toy cars cost 440 dollars. What is the price of 1 red toy car and 1 blue toy car each? 1 red toy car □ 1 blue toy car □
Answer: 60dollars, 40dollars
