Muthu, Ali and Bill shared a sum of money. 30% of Muthu's share was equal to 80% of Ali's share. Bill's share was 25% 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 percent of Bill's share was Ali's share? Round off your answer to 1 decimal place.

.3M=.8A

B=.25M
A-185=B

find A+B+M

starting with last equation, then substuting

A-185=B
.3/.8 M-185=.25M

.3M-.8*185=.8*.25 M
.3M-.2M=.8*185
.1M=148
M=1480

check that, then solve for B, and A

Let their respective amounts be m, a and b

30% of Muthu's share equals 80% of Ali's share
.3m = .8a
3m = 8a
m = 8a/3

Bill's share was 25% of Muthus share
b = .25 m
4b = m

Ali had $185 more than Bill
a = b+185 or b = a-185

but since m = 8a/3 and m = 4b
8a/3 = 4b
times 3
8a = 12b
sub in b = a-185
8a = 12(a-185)
8a = 12a - 2220
-4a = -2220
a = 555
then b = 555-185 = 370
m = 4b = 4(370) = 14800

So Muthu had 1480
Ali had 555
Bill had 370
for a total of $2405


check: does Ali have 185 more than Bill ? YES
is 30% of 1480 , or 444
equal to .8(555) or 444 , YEAHHH

b) now that we have the actual amounts, I am sure you can handle b)

Salisu Timi

1123675

To solve this problem, let's break it down step by step.

Step 1: Set up the equations.
Let's say the total sum of money is X.
Muthu's share = M
Ali's share = A
Bill's share = B

From the information given:
Equation 1: 30% of M = 80% of A
Equation 2: B = 25% of M
Equation 3: A = B + $185

Step 2: Solve the equations.
Let's solve the equations in order to find the values of M, A, and B.

From Equation 1, we have:
0.3M = 0.8A
Divide both sides of the equation by 0.3:
M = (0.8A) / 0.3
Simplify further:
M = 2.67A

From Equation 2, we have:
B = 0.25M
Replace M in this equation with its value from Equation 1:
B = 0.25 * 2.67A
Simplify further:
B = 0.667A

From Equation 3, we have:
A = B + $185
Since we found the value of B in terms of A in the previous equation, we can substitute it in:
A = 0.667A + $185
Subtract 0.667A from both sides of the equation:
0.333A = $185
Divide both sides of the equation by 0.333:
A = $555
Now that we have found the value of A, we can calculate the values of M and B using Equations 1 and 2.

From Equation 1:
M = 2.67A
Substitute the value of A:
M = 2.67 * $555
M ≈ $1482

From Equation 2:
B = 0.25M
Substitute the value of M:
B = 0.25 * $1482
B ≈ $370.5

Step 3: Calculate the total sum of money.
To find the total sum of money, we add the shares of Muthu, Ali, and Bill:
Total sum = M + A + B
Total sum = $1482 + $555 + $370.5
Total sum ≈ $2407.5

Therefore, the total sum of money is approximately $2407.5.

Step 4: Find the percentage of Bill's share in comparison to Ali's share.
To find the percentage of Bill's share compared to Ali's share, we need to calculate (Bill's share / Ali's share) * 100.

Bill's share = $370.5
Ali's share = $555

Percentage = (Bill's share / Ali's share) * 100
Percentage = ($370.5 / $555) * 100
Percentage ≈ 66.67%

Therefore, Ali's share is approximately 66.7% of Bill's share.