Point e is between points d and f. if de = x − 2, ef = 6x + 4, and df = 8x − 2, find x

DE + EF = DF

x - 2 + 6x + 4 = 8x - 2
7x + 2 = 8x - 2
2 + 2 = 8x - 7x
4 = x <===

4 nickle, 4 dime and 3 (11-2*4) quarters.

Explanation: Quarters (q) = 25 cent, nickles (n) = 10 cent, dime (d) = 5 cent:

q + n + d = 11 coins
25*q + 10*n + 5*d = 135 cents
d = n

Then:

q + 2n = 11 and 25q + 15n = 135

q+2n=11 and 5q + 3n = 27

q = 11-2n > 5*(11-2n)+3n = 27

55 -10n+3n=27, or -7n = -28, n = 4 (nice!)

So, 4 nickle, 4 dime and 3 (11-2*4) quarters.

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