Ray's New Practical Arithmetic · Art. 229 · Unit 23: Partnership, Equation of Payments and Average
107. Partnership with time
Goal: Your child shares a gain or loss when partners' money was in the business for different lengths of time.
You'll need
- Paper and pencil, or a slate or small whiteboard
What's in the book
Page 294 gives Partnership with Time (Art. 229) with two worked examples, the rule and problems. Page 295 has three more problems. Answers are printed.
The lesson, step by step
Warm-up
Ask: Is $100 used for 2 months the same as $200 used for 1 month? Why might it be?
Work the book's examples
A and B built a wall for $82; A had 4 men at work 5 days, and B 3 men 7 days: how should they divide the money?
4 men for 5 days is like 20 men for 1 day; 3 men for 7 days is like 21. Divide $82 in the ratio 20 to 21: A $40, B $42.
A put in trade $50 for 4 mo.; B, $60 for 5 mo.; they gained $24: what was each man's share?
$50 × 4 = $200 for 1 month; $60 × 5 = $300 for 1 month. Divide $24 as 2 to 3: $9.60 and $14.40.
The rule
Multiply each partner's stock by the time it was employed; then take such part of the gain or loss as each partner's product is part of the sum of all the products.
Guided practice
Do this one together:
A and B hire a pasture for $54: A pastures 23 horses 27 da.; B, 21 horses 39 da.: what will each pay?
(23 × 27 = 621 "horse-days"; 21 × 39 = 819.)
Independent practice and check
Your child works the remaining problems on pages 294–295, including the pasture with cows and the partners who put in and drew out money. The book prints the answer at the end of each problem line. Have your child cover the answers with a strip of paper, work the problem, then slide the strip down to check.
Mental-math wrap-up
Aloud: $100 for 3 months is like how much for 1 month? Two partners: $300 for 2 months and $200 for 3 months. How should they share?