Math Drills
Various Word Problems Review
B-4Word Problems (Age Problems, etc.)
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What this worksheet covers
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.
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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.
- Patterns and Regularity · The Color at a Given Position2 questions
- How Savings Grow · Savings (Basics)1 question
- How Savings Grow · Catching Up1 question
- Age Problems · Years Later1 question
Questions & answers
Problems and answers on this worksheet
These are the problems in “Various Word Problems”, shown with their answers.
(1)White, yellow, and red color boards are arranged repeatedly in the order white, yellow, white, red, red, white, yellow, white, red, red, and so on. What color is the 37th board from the left? Answer □
Answer: yellow
(2)Red, blue, and yellow sheets of paper are arranged repeatedly in the order red, blue, red, yellow, red, blue, red, yellow, and so on. What color is the 31st sheet from the left? Answer □
Answer: red
(3)Starting next month, Riley will save 80 dollars each month, and Hannah will save 120 dollars each month. After how many months will the total savings of the 2 people be exactly 800 dollars? Answer □
Answer: 4months later
(4)The older brother has 1000 dollars and the younger brother has 400 dollars now. Starting next month, the older brother will save 100 dollars and the younger brother will save 250 dollars every month. After how many months will the savings of the 2 people be the same amount? Answer □
Answer: 4months later
(5)The father is 36 years old, and the child is 12 years old. In how many years later will the father's age be 2 times the child's age? Answer □
Answer: 12years later
What to do next
More worksheets in this unit
How Savings GrowHow Savings Grow Word Problems
Work-Rate ProblemsWork-Rate Problems Word Problems
Crane and Turtle ProblemsCrane and Turtle Problems Word Problems
Elimination ProblemsElimination Problems Word Problems
Age ProblemsAge Problems Word Problems
Various Word Problems ReviewVarious Word Problems Review Word Problems (Work Rate, etc.)
