James and Daniel are owners of J.D chemicals shared their end of the year profit in the ratio of 4:6.if Daniel got $4000 more than James, Calculate their total annual profit
Options
A.N22,000
B.N14,000
C.N16,000
D.N20,000?
J = James´s profit
D = Daniel´ s profit
Daniel got $4000 more than James mean:
D = J + 4000
J / D = 4 / 6 = 2 ∙ 2 / 2 ∙ 3 = 2 / 3
J / D = 2 / 3
Cros multiply
3 J = 2 D
Divide both sides by 2
3 J / 2 = D
D = 3 J / 2
D = J + 4000
D = D
3 J / 2 = J + 4000
Subtract J to both sides
3 J / 2 - J = 4000
3 J / 2 - 2 J / 2 = 4000
J / 2 = 4000
Multiply both sides by 2
J = $ 8000
D = J + 4000 = 8000 + 4000
D = $ 12000
Total profit = J + D = $ 8000 + $ 12000 = $ 20000
Proof:
J / D = 8000 / 12000 = 4000 ∙ 2 / 4000 ∙ 3 = 2 / 3
D = $ 12000 = J + $ 4 000 = $ 8000 + $ 4000
Jame's profit --- 4x
Daniel's profit --- 6x
6x-4x = 4000
x = 2000
total profit = 10x = 20,000
James got $X.
Daniel got $(x+4,000).
x/(x+4,000) = 4/6,
6x = 4x + 16,000,
X = $8,000.
x+4000 = 8,000 + 4,000 = $12,000.
Total profit = 8,000 + 12,000 = $20,000.
To calculate the total annual profit, we need to find the amount each owner received based on the given ratio and additional amount.
Let's assume James' share of the profit is x dollars.
According to the given ratio of 4:6, Daniel's share of the profit would be 6/4 times James' share.
Daniel's share = (6/4) * x = 1.5x
We also know that Daniel received $4000 more than James, so we can set up the following equation:
1.5x - x = $4000
Simplifying the equation, we have:
0.5x = $4000
To isolate x, we can divide both sides of the equation by 0.5:
x = $4000 / 0.5
x = $8000
So, James' share of the profit is $8000.
To find Daniel's share, we can multiply James' share by 1.5:
Daniel's share = 1.5 * $8000 = $12000
Now, to calculate the total annual profit, we add James' and Daniel's shares:
Total annual profit = James' share + Daniel's share
= $8000 + $12000
= $20000
Therefore, their total annual profit is $20,000.