SOLUTION: a).the ratio of james to john's earning was 4:3. james's earning rose to kshs. 7200 after an increase of 10%. calculate the percentage increase in john's earnings given that the su

Algebra ->  Finance -> SOLUTION: a).the ratio of james to john's earning was 4:3. james's earning rose to kshs. 7200 after an increase of 10%. calculate the percentage increase in john's earnings given that the su      Log On


   

Question 1185930: a).the ratio of james to john's earning was 4:3. james's earning rose to kshs. 7200 after an increase of 10%. calculate the percentage increase in john's earnings given that the sum of their new earnings was kshs. 15600
b).james and john contributed all the new earnings to buy maize at kshs.1175 per bag. the maize was then sold at kshs. 1762.50 per bag. They shared all the money from the sales in the ratio of contributions. calculate the amount james received
Answer by CPhill(1987) About Me  (Show Source):
You can put this solution on YOUR website!
Here's how to break down this problem:
**a) Percentage Increase in John's Earnings**
1. **James' Initial Earnings:** James' earnings increased by 10% to 7200 kshs. Let 'x' be his initial earnings.
* x + 0.10x = 7200
* 1.10x = 7200
* x = 7200 / 1.10
* x ≈ 6545.45 kshs
2. **John's Initial Earnings:** The ratio of James' to John's earnings was 4:3.
* John's initial earnings = (3/4) * James' initial earnings
* John's initial earnings = (3/4) * 6545.45
* John's initial earnings ≈ 4909.09 kshs
3. **John's New Earnings:** The sum of their new earnings was 15600 kshs.
* John's new earnings = Total new earnings - James' new earnings
* John's new earnings = 15600 - 7200
* John's new earnings = 8400 kshs
4. **Percentage Increase in John's Earnings:**
* Percentage increase = [(New earnings - Initial earnings) / Initial earnings] * 100
* Percentage increase = [(8400 - 4909.09) / 4909.09] * 100
* Percentage increase ≈ 71.1%
**b) James' Share of Sales Money**
1. **Total Contributed:** James and John contributed their new earnings, totaling 15600 kshs.
2. **Bags of Maize Purchased:**
* Bags purchased = Total contributed / Cost per bag
* Bags purchased = 15600 / 1175
* Bags purchased = 13.27 bags. Since you can't buy parts of bags, we'll use 13 bags.
3. **Total Revenue from Sales:**
* Total revenue = Bags sold * Selling price per bag
* Total revenue = 13 * 1762.50
* Total revenue = 22912.50 kshs
4. **Total Profit:**
* Profit = Total revenue - Total cost
* Profit = 22912.50 - 15600
* Profit = 7312.50 kshs
5. **James' Share:** James' share is proportional to his contribution.
* James' share = (James' new earnings / Total new earnings) * (Total Revenue)
* James' share = (7200 / 15600) * 22912.50
* James' share ≈ 10565.38 kshs
**Therefore:**
* **a)** John's earnings increased by approximately **71.1%**.
* **b)** James received approximately **10565.38 kshs** from the maize sales.