# Yosie, Maya, Noah & Datan shared $168. Datan received 1/7 of the total amount of money received by Yosie, Noah & Maya. Yosie received 3/4 of the total amount of money received by Noah and Maya. Maya received 2/5 as much as Noah. How much did Maya receive?

Maya eceived

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Let's denote the amount received by Yosie, Maya, Noah, and Datan as Y, M, N, and D respectively.

Given:

- Y + M + N + D = $168
- D = 1/7(Y + N + M)
- Y = 3/4(N + M)
- M = 2/5N

Using equation 4, we can express M in terms of N: M = 2/5N.

Substitute M in equation 3: Y = 3/4(N + 2/5N).

Now, solve equation 3 for Y: Y = 3/4(7/5N).

Y = 21/20N.

Now, substitute the expression for Y in equation 2: D = 1/7(21/20N + N + 2/5N).

D = 1/7(107/20N).

We know that D + Y + M + N = $168, so let's express D in terms of N:

D = $168 - (21/20N + 2/5N + 3/4(7/5N)).

D = $168 - (21/20N + 2/5N + 21/20N).

D = $168 - (63/20N).

Now, let's add up all the individual amounts to get the total:

Y + M + N + D = (21/20N) + (2/5N) + N + (168 - 63/20N).

168 = (21/20N) + (2/5N) + N + (168 - 63/20N).

Solve for N:

168 = 101/20N + N + 168 - 63/20N.

0 = 101/20N + N - 63/20N.

0 = (101/20 - 63/20)N + N.

0 = (38/20)N + N.

0 = (38/20 + 20/20)N.

0 = (58/20)N.

N = 0.

Substitute N = 0 into equation 4 to find M:

M = 2/5(0).

M = $0.

Maya received $0.

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