30
Chapter III review problems
Textbook: Part 1, lesson 30, pp. 114–117
GoalReview Chapter III word problems: equalizing, parts, formulas, motion, economics, work.
New words
formula · formulaspeed of approach · yaqinlashish tezligiproductivity · mehnat unumdorligione-part method · bir qism usuli
Explanation
We solve a word problem in four stages: read, plan, solve, check. In “how many times more” problems take the smaller quantity as 1 part. Formulas: P = 2(a + b), S = a · b, S = v · t, C = p · n, A = N · t. In each, the rule for an unknown factor gives the inverse problems. In two-body motion, speeds are added when the bodies move apart or towards each other and subtracted when one chases the other in the same direction. In joint work the productivities add.
Worked examples
Two drivers set out towards each other from 270 km apart at 60 and 75 km/h. Speed of approach is 135 km/h, so they meet after 270 : 135 = 2 hours.
A rectangle has perimeter 46 cm and width 8 cm: length 46 : 2 − 8 = 23 − 8 = 15 cm, area 15 × 8 = 120 cm².
Class activity
“Formula lotto”: cards with formulas and problems are mixed; pupils match each problem to its formula and calculate the answer.
Practice
1
A rectangle has perimeter 46 cm and width 8 cm. Find its length (cm).
15
2
Two cars set out from 270 km apart towards each other at 60 and 75 km/h. After how many hours do they meet?
2
3
Two packets hold 1 350 g of sweets, one twice the other. How many grams in the larger packet?
900
4
What do the formulas S = v · t, C = p · n and A = N · t have in common?
In all three a value per unit (speed, price, productivity) is multiplied by an amount to get the total.