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.