Mary, Margaret, Ron and Nick are to share a sholarship. Ron receives 1/3 of the scholarship; Nick gets 1/4 of the scholarship; Mary receives the same as Nick, and Margaret receives $72,000. Find each person's share in the scholarship as well as the original scholarship amount.

Question

Mary, Margaret, Ron and Nick are to share a sholarship. Ron receives 1/3 of the scholarship; Nick gets 1/4 of the scholarship; Mary receives the same as Nick, and Margaret receives $72,000. Find each person's share in the scholarship as well as the original scholarship amount.

You must use a Let statement.
State the equation for the above situation
Solve Algebraicially

Answer 1

1 - 1/3 - 1/4 - 1/4 = 1/6

so, 72000 is 1/6 of the total.
The total is thus 432,000

1/3 = 144,000
1/4 = 108,000

You can massage the answer to the required format.

Answer 2

Thanks. I figuired out the working, but not sure how to use the Let statement. Would it be correct to say

Let A = original scholarship amount
A = 1-1/3 -1/4-1/4 x72,000
A = 1/6 x 72 = 432,000

Answer 3

Better would be

(1 - 1/3 - 1/4 - 1/4) A = 72000
1/6 A = 72000
A = 6*72000

or

A = 72000/(1 - 1/3 - 1/4 - 1/4)

Answer 4

Let's solve this problem step by step using a Let statement and algebraic equations.

Let's assume the original scholarship amount is x dollars.

According to the given information:
Ron receives 1/3 of the scholarship, which is (1/3)x dollars.
Nick receives 1/4 of the scholarship, which is (1/4)x dollars.
Mary receives the same amount as Nick, which is also (1/4)x dollars.
Margaret receives $72,000.

Now, let's set up an equation to represent the situation:
(1/3)x + (1/4)x + (1/4)x + 72000 = x

Combine like terms:
(7/12)x + 72000 = x

To get rid of the denominators, we can multiply the entire equation by 12:
12 * (7/12)x + 12 * 72000 = 12 * x
7x + 864000 = 12x

Next, we will move all the variables to one side of the equation and the constants to the other side to solve for x:
12x - 7x = 864000
5x = 864000

Now, we can solve for x by dividing both sides of the equation by 5:
x = 864000 / 5
x = 172800

Therefore, the original scholarship amount is $172,800.

Now, let's plug this value of x back into the equations to find each person's share in the scholarship:

Ron's share: (1/3) * x = (1/3) * 172800 = $57,600
Nick's share: (1/4) * x = (1/4) * 172800 = $43,200
Mary's share: (1/4) * x = (1/4) * 172800 = $43,200
Margaret's share: $72,000

So, each person's share in the scholarship is:
Ron: $57,600
Nick: $43,200
Mary: $43,200
Margaret: $72,000

And the original scholarship amount is $172,800.