The ratio of Juma’s and Akinyi's earnings was 5:3. Juma’s earnings rose to shilling 8400 after an increase of 12%. Calculate the percentage increase in Akinyi’s earning given that the sum of their new earnings was shilling 14100.
(b) Juma and Akinyi contribute all the new earnings to buy maize at shilling 1175 per bag. The maize was then sold at shilling 1762.50 per bag. The two shared all the money from the sales of the maize in the ratio of their contributions. Calculate the amount that Akinyi got.
1.12j = 8400
j = 7500
j/a = 5/3
a = 3/5 j = 4500
(14100-8400)/4500 = 1.267
so, Akinyi's money grew by 26.7%
First, let's find the original earnings of Juma and Akinyi.
If the ratio of Juma's and Akinyi's earnings was 5:3, we can set up the equation:
5x + 3x = 14100
8x = 14100
x = 1762.50
So, Juma's original earnings were 5 * 1762.50 = 8812.50 shillings,
and Akinyi's original earnings were 3 * 1762.50 = 5287.50 shillings.
Next, we'll calculate the new earnings after the increase for both Juma and Akinyi.
Juma's earnings increased by 12%, so his new earnings are 8812.50 + 12% of 8812.50:
8812.50 + 0.12 * 8812.50 = 8812.50 + 1057.50 = 9870 shillings.
The sum of their new earnings is given as 14100 shillings, so we can find Akinyi's new earnings:
Akinyi's new earnings = 14100 - Juma's new earnings
= 14100 - 9870
= 4230 shillings.
Now, let's calculate the percentage increase in Akinyi's earnings.
Percentage increase = ((new earnings - original earnings) / original earnings) * 100%
= ((4230 - 5287.50) / 5287.50) * 100%
= (-1057.50 / 5287.50) * 100%
≈ -20% (approximately)
So, Akinyi's earnings decreased by approximately 20%.
For the second part of the question, we'll calculate the amount that Akinyi got from the maize sales.
Juma and Akinyi contributed all the new earnings, which totaled 14100 shillings, to buy maize at 1175 shillings per bag.
So, they were able to buy 14100 / 1175 = 12 bags of maize.
They sold the maize at 1762.50 shillings per bag.
The total amount from the sales of the maize was 12 * 1762.50 = 21150 shillings.
Now, let's calculate the ratio of their contributions:
Juma's contribution = 9870 shillings
Akinyi's contribution = 4230 shillings
The ratio of their contributions is 9870 : 4230, which simplifies to 2.33 : 1.
To determine the amount that Akinyi got, we'll divide the total amount from the sales of the maize by the sum of the ratios.
Akinyi's share = (4230 / (9870 + 4230)) * 21150
= (4230 / 14100) * 21150
≈ 0.30 * 21150
≈ 6345 shillings (approximately)
Therefore, Akinyi received approximately 6345 shillings from the maize sales.
Let's solve this step by step:
(a) We are given that the ratio of Juma's and Akinyi's earnings was 5:3. Let's represent Juma's earnings as 5x and Akinyi's earnings as 3x.
Juma's earnings rose to 8400 shillings after an increase of 12%. To calculate his original earnings, we can use the formula: (Original earnings) * (1 + Increase percentage) = New earnings.
Therefore, 5x * (1 + 0.12) = 8400.
Simplifying the equation, we have 5.6x = 8400.
Dividing both sides by 5.6, we get x = 8400 / 5.6 = 1500.
Now we can find Akinyi's original earnings: 3x = 3 * 1500 = 4500 shillings.
The sum of their new earnings is given to be 14100 shillings.
Therefore, Juma's new earnings are 8400 shillings, and Akinyi's new earnings are 14100 - 8400 = 5700 shillings.
To calculate the percentage increase in Akinyi's earnings, we can use the formula: (Increase amount / Original amount) * 100.
The increase amount in Akinyi's earnings is 5700 - 4500 = 1200 shillings.
Therefore, the percentage increase is (1200 / 4500) * 100 = 26.67%.
(b) Juma and Akinyi contribute all their new earnings, which are 8400 and 5700 shillings respectively, to buy maize at 1175 shillings per bag.
Let's calculate the number of bags they can buy separately.
The number of bags Juma can buy = 8400 / 1175 = 7.15 bags (approximately).
The number of bags Akinyi can buy = 5700 / 1175 = 4.85 bags (approximately).
Since the number of bags cannot be in decimal points, let's round down both values to the nearest whole number.
Juma can buy 7 bags, and Akinyi can buy 4 bags.
When they sell the maize at 1762.50 shillings per bag, they will share the money in the ratio of their contributions: 7:4.
Let's calculate the total amount from the sales of the maize: (Total bags) * (Selling price per bag).
Total amount = (7 + 4) * 1762.50 = 11 * 1762.50 = 19387.50 shillings.
To calculate Akinyi's share, we can use the ratio of their contributions: 4 / (7 + 4) * Total amount.
Akinyi's share = (4 / 11) * 19387.50 = 4 * 1762.50 ≈ 7050 shillings.
Therefore, Akinyi got approximately 7050 shillings from the sales of the maize.
To solve this problem, we'll break it down into two parts.
Part 1: Finding the new earnings of Akinyi
Given that the ratio of Juma's and Akinyi's earnings was 5:3, we can calculate Juma's earnings before the increase. Since his earnings rose to shilling 8400 after a 12% increase, we can find his earnings before the increase by dividing 8400 by (1 + 12/100) to account for the 12% increase.
Juma's earnings before the increase = 8400 / (1 + 12/100) = 8400 / 1.12 = 7500
Now we know Juma's earnings before the increase, we can find Akinyi's earnings before the increase using the given ratio.
Akinyi's earnings before the increase = (3/5) * Juma's earnings before the increase = (3/5) * 7500 = 4500
We know that the sum of their new earnings is shilling 14100, so we can subtract Juma's new earnings (8400) from the sum to find Akinyi's new earnings.
Akinyi's new earnings = Sum of new earnings - Juma's new earnings = 14100 - 8400 = 5700
To calculate the percentage increase in Akinyi's earnings, we need to find the difference between her new earnings and her earnings before the increase, and then divide it by her earnings before the increase.
Percentage increase in Akinyi's earnings = ((Akinyi's new earnings - Akinyi's earnings before the increase) / Akinyi's earnings before the increase) * 100
= ((5700 - 4500) / 4500) * 100
= 1200 / 4500 * 100
= 26.67%
Therefore, the percentage increase in Akinyi's earnings is approximately 26.67%.
Part 2: Calculating the amount that Akinyi got from the sales of the maize
Since Juma and Akinyi contributed all their new earnings to buy maize, we can find the total amount they contributed by adding their new earnings.
Total contribution = Juma's new earnings + Akinyi's new earnings = 8400 + 5700 = 14100
Given that Juma and Akinyi shared all the money from the sales of the maize in the ratio of their contributions, we can find the amount that Akinyi got by multiplying the total sales of maize by her contribution ratio.
Amount Akinyi got = (Akinyi's contribution / Total contribution) * Total sales of maize
= (5700 / 14100) * Total sales of maize
We know that the maize was sold at shilling 1762.50 per bag. Since the amount Akinyi got is proportional to the sales of maize, we can find her share by multiplying the amount she got with the sales of maize.
Amount Akinyi got = (5700 / 14100) * Total sales of maize = 1762.50 * (5700 / 14100) * Total sales of maize
Now, we can solve for Total sales of maize by dividing both sides by (1762.50 * (5700 / 14100)).
Total sales of maize = (Amount Akinyi got) / (1762.50 * (5700 / 14100))
Calculating this will give you the amount that Akinyi got from the sales of the maize.