Jada, Nicholas, Nita, and Calvin shared $60. Jada received 1/2 of the total amount of money Nicholas, Nita, and Calvin received. Nicholas received 2/3 of the total amount of money Nita and Calvin received. Nita received 3 times as much as calvin.

Question

Jada, Nicholas, Nita, and Calvin shared $60. Jada received 1/2 of the total amount of money Nicholas, Nita, and Calvin received. Nicholas received 2/3 of the total amount of money Nita and Calvin received. Nita received 3 times as much as calvin.

(a) how much money did jada receive?
(b) how much more money did nicholas receive than calvin?

Answer 1

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

Step 1: Assign variables
Let's assign variables to represent the amounts of money each person received:

Jada's amount = J
Nicholas's amount = N
Nita's amount = x
Calvin's amount = C

Step 2: Set up equations
From the given information, we can set up the following equations:

J = (1/2) * (N + x + C) (Jada received half of the total amount)
N = (2/3) * (x + C) (Nicholas received two-thirds of the total amount received by Nita and Calvin)
x = 3C (Nita received three times as much as Calvin)

Step 3: Solve for the variables

From the third equation, we can substitute x in terms of C into the second equation:

N = (2/3) * (3C + C)
N = (2/3) * 4C
N = (8/3) * C

Now substitute the values of N and x into the first equation:

J = (1/2) * ((8/3) * C + 3C + C)
J = (1/2) * ((8/3) * C + 4C)
J = (1/2) * (20/3) * C
J = (10/3) * C

Step 4: Find the values of the variables

To find the value of C, we consider that Jada, Nicholas, Nita, and Calvin shared $60 in total:

J + N + x + C = 60

Substituting the values of J and N in terms of C:

(10/3) * C + (8/3) * C + 3C + C = 60

Combining like terms:

(10C + 8C + 9C + 3C) / 3 = 60
(30C) / 3 = 60
10C = 60
C = 6

Now substitute the value of C back into the equations to find the other variables:

x = 3C = 3 * 6 = 18
N = (8/3) * C = (8/3) * 6 = 16
J = (10/3) * C = (10/3) * 6 = 20

Step 5: Answer the questions

(a) Jada received $20.
(b) Nicholas received $16, and Calvin received $6. Thus, Nicholas received $10 more than Calvin.

Therefore, the answers are:
(a) Jada received $20.
(b) Nicholas received $10 more than Calvin.

Answer 2

J+Nk+Ni+C=60

J=1/2 (Nk+Ni+C)
Nk=2/3 (Ni+C)
Ni=3C

take first equation,put second in it.

3/2 Nk + 3/2Ni+3/2C=60
or Nk+Ni+C=40

Then J=20*****

Now take
Nk=2/3 (Ni+C)
Ni=3C
to get Nk=2/3(4C=8/3 C
But 20=1/2 (Nk+Ni+C) or
40=8/3 C + 3C + C so figure C...