3 boys, Aaron, Benny and Charles, share a sum of money. Aaron receives 40% of the sum of money. Benny receives 3 times as much as Charles and $29 more than Aaron.
a.) What percentage of the sum of money does Charles get?
b.) What is the total sum of money given to the 3 boys?
Sum = $X.
Aaron = 0.4x.
Benny = (0.4x+29).
Charles = (0.4x+29)/3.
a. 0.4x + (0.4x+29) + (0.4x+29)/3 = $X.
Multiply both sides by 3:
1.2x + 1.2x + 87 + 0.4x + 29 = 3x
2.8x - 3x = -116
-0.2x = -116
X = $580.
Charles = (0.4*580+29)/3 = $87.
Charles % = (87/580)*100% = 15.
b. Total = X = $580.
Let's assume the total sum of money is "x".
a.) To find the percentage of the sum of money Charles gets, we first need to find the amount Benny receives.
Benny receives $29 more than Aaron, so Benny's share is Aaron's share plus $29:
Benny's share = Aaron's share + $29
Benny's share = 40% of x + $29
We also know that Benny's share is 3 times as much as Charles's share:
Benny's share = 3 * Charles's share
We can set up the equation:
40% of x + $29 = 3 * Charles's share
To find Charles's share, we need to rearrange the equation:
Charles's share = (40% of x + $29) / 3
Now, let's find the percentage of the sum of money Charles gets:
Percentage of sum of money Charles gets = (Charles's share / x) * 100
Percentage of sum of money Charles gets = ((40% of x + $29) / 3) / x * 100
b.) To find the total sum of money given to the 3 boys, we need to add up the individual shares of Aaron, Benny, and Charles:
Total sum of money given to 3 boys = Aaron's share + Benny's share + Charles's share
Total sum of money given to 3 boys = 40% of x + 40% of x + $29 + (40% of x + $29) / 3
Simplifying the expression further will give us the total sum of money given to the 3 boys.
To find the answers to these questions, we can start by assigning variables and setting up equations to represent the given information.
Let's assume the total sum of money is represented by "x" dollars.
According to the given information:
- Aaron receives 40% of the sum, which is 0.4x dollars.
- Benny receives 3 times as much as Charles, let's call Charles' share "y" dollars. So Benny's share is 3y dollars.
- Benny also receives $29 more than Aaron, which means Benny's share is Aaron's share plus $29. Thus, 3y = 0.4x + 29.
Now let's solve these equations step by step:
a.) To find the percentage Charles gets, we need to determine his share relative to the total sum. Since Aaron gets 40%, Benny gets 3y and Charles gets y, the total percentage should be 100%. Therefore:
100% - 40% - 3y = y
60% = 4y
To get the value of y, we can divide both sides of the equation by 4:
y = 60% / 4 = 15%
So, Charles gets 15% of the sum.
b.) To find the total sum of money, we need to consider Aaron's share, Benny's share, and Charles' share and sum them up.
Aaron's share = 0.4x
Benny's share = 3y = 3 * 15% of x
Charles' share = y = 15% of x
Total sum of money = Aaron's share + Benny's share + Charles' share
Total sum of money = 0.4x + 3(15% of x) + 15% of x
Total sum of money = 0.4x + 0.45x + 0.15x
Total sum of money = 1x = x
Therefore, the total sum of money is x dollars.
To find the exact value of x, we need additional information or equations related to the problem. With the given information, we cannot determine the exact value of x.