17
Solving harder problems
Textbook: Part 1, lesson 17, pp. 66–69
GoalSolve harder word problems by the equalizing method and by writing an equation.
New words
equalizing method · tenglashtirish usulidiagram model · model-sxemashare (part) · hissaassumption method · faraz qilish usuli
Explanation
A harder problem can be solved in two ways. In the equalizing method we remove the excess from the larger part, the parts become equal, and the remaining total is split equally. In the equation method we call the smaller part x, write the other parts using x and, with a diagram, build an equation: x + (x + 12) = 80 or x + 4x = 150. In problems like “2 shares and 3 shares” take one share as x and write 2x + 3x = 5x. In the assumption method we first suppose all creatures are of one kind, then correct the difference. Always check the answer against the conditions.
Worked examples
Two classes have 62 pupils in total, the first has 4 more. Equalize: 62 − 4 = 58, 58 : 2 = 29. So the classes have 29 and 33. Check: 29 + 33 = 62.
200 notebooks were sold in two weeks, 4 times as many in the second week as in the first. x + 4x = 200, 5x = 200, x = 40. So 40 in the first week and 160 in the second.
Class activity
“Draw the diagram”: groups read a problem, draw a segment diagram, then form and solve an equation and check the answer.
Practice
1
Two pieces of wire total 90 m; the second is 18 m longer than the first. How long is the first one (m)?
36
2
Solve x + 4x = 275.
55
3
Flour and sugar are mixed in shares 3 : 2 and the mixture is 1 000 g. How many grams of sugar?
400
4
Why do we subtract the difference from the total and divide by 2 in the equalizing method?
After the extra difference is removed from the larger part, both parts are equal, so the remaining total splits into two equal parts.