Muthu, Ali and Bill shared a sum of money. 3/10 of Muthu's share was equal to 4/5 of Ali's share. Bill's share was 1/4 of Muthu's share. Ali had $185 more than Bill.
(a) Find the total sum of money.
(b) If Muthu gave Bill 55% of his share, what percentage of Bill's share was Ali's share? Round off your answer to 1 decimal place.
(a) Total sum of money = $1,080
(b) Percentage of Bill's share that was Ali's share = 33.3%
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I'm sorry, could you please provide more information so I can assist you better?
To solve this problem, we can break it down into steps:
Step 1: Setup a system of equations.
Step 2: Solve the equations simultaneously to find the unknowns.
Step 3: Use the solutions to answer the given questions.
Let's start with step 1:
Let M represent Muthu's share, A represent Ali's share, and B represent Bill's share.
From the information given, we can write the equations:
Equation 1: 3/10 * M = 4/5 * A
Equation 2: B = 1/4 * M
Equation 3: A = B + 185
Now, let's move on to step 2 and solve the equations simultaneously:
From Equation 1, we can simplify it by multiplying both sides by 10/3:
M = (10/3) * (4/5) * A
M = (8/3) * A
Let's call this Equation 4.
Substituting Equation 4 into Equation 2, we get:
B = 1/4 * [(8/3) * A]
B = 2/3 * A
Let's call this Equation 5.
Substituting Equation 5 into Equation 3, we get:
A = (2/3 * A) + 185
A - (2/3 * A) = 185
(1/3 * A) = 185
A = 185 * 3
A = 555
Let's call this Equation 6.
Now, substituting the value of A back into Equation 5, we can solve for B:
B = 2/3 * 555
B = (2 * 555)/3
B = 370
Let's call this Equation 7.
Finally, substituting the values of A and B into Equation 4, we can solve for M:
M = (8/3) * 555
M = (8 * 555)/3
M = 1480
Let's call this Equation 8.
Now, let's move on to step 3 and answer the given questions:
(a) The total sum of money is the sum of M, A, and B:
Total sum = M + A + B
Total sum = 1480 + 555 + 370
Total sum = 2405
So the total sum of money is $2405.
(b) If Muthu gave Bill 55% of his share, then Bill's share becomes 45% of Muthu's share.
Bill's share = 0.45 * M
To find the percentage of Bill's share that is Ali's share, we can divide Ali's share by Bill's share and multiply by 100:
Percentage = (A/B) * 100
Percentage = (555/0.45M) * 100
Using the value of M from Equation 8, we can calculate the percentage:
Percentage = (555/0.45 * 1480) * 100
Percentage = (555/666) * 100
Percentage = 83.33
Rounding off to 1 decimal place, the percentage of Bill's share that is Ali's share is approximately 83.3%.