A 106 - in. board is cut into three pieces. The shortest length is two -thirds of the midsize length and the longest length is 15 in. less than two times the midsize length. Find the length of each piece what is the solution

Short length=2/3 (midsize length)................eqn 1

longest length=2*(midsize)-15....................eqn 2

short + mid+ long= 106................................eqn 3

substitute for short and long in third eqn

2/3 (mid) + mid +2(mid) -15 = 106

3 and 2/3 mid = 121

11/3 mid =121

mid = 363/11

mid = 33

plug into eqn 1 and eqn 2

Short length=2/3 (33)

short= 22

longest length=2*(33)-15

long=51

Solution (22, 33, 51)

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