Ray's New Higher Arithmetic · Art. 358 · Unit 23: Partnership
103. Partnership: shares for different times
Goal: Your student divides a gain when partners' money was in the business for different lengths of time.
You'll need
- The book
- A slate, small whiteboard or scrap paper
- A notebook and pencil
What's in the book
Case II, with a worked problem, a rule and examples, including a puzzle about pumping out a cistern. Answers are printed.
The lesson, step by step
Warm-up
Ask: Is $100 in the business for 1 month worth as much as $100 for 6 months?
The idea
Read:
To apportion the gain or loss when the full shares are not continued through the same period.
SayMoney times months is the fair measure.
Work the book's example
A, B, and C are partners; A puts in $2500 for 8 mo.; B, $4000 for 6 mo.; C, $3200 for 10 mo.; their net gain is $4750: divide the gain.
$2500 × 8 = 20000; $4000 × 6 = 24000; $3200 × 10 = 32000. Total 76000. A gets 20/76 of $4750 = $1250, B $1500, C $2000.
The rule
Read:
Multiply each partner's stock by the time it is used; and divide the gain or loss in proportion to the products so obtained.
Guided practice
A begins business with $6000; at the end of 6 mo. he takes in B, with $10000; 6 mo. after, their gain is $3300: what is each share?
Independent practice and check
Your student works the rest, including the pump problem, and checks the printed answers.
Wrap-up
Ask: In the pump problem, what plays the part of the money? (The strokes each man made.)