Mattie's house consists of two stories and an attic. The first floor is #8 5/6# feet tall, the second floor is #8 1/2# feet tall, and the entire house is #24 1/3# feet tall. How tall is the attic?

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Answer 1 · 2018-03-28T04:02:46

The attic is #7# feet tall

So the total house height is the first floor plus the second floor plus the attic

#H_T = F_1 + F_2 +A#

#A = H_T - F_1 - F_2#

where #H_T = 24 1/3# or #73/3#

#color(white)(where )# #F_1 = color(white)(/) 8 5/6# or #53/6#

#color(white)(where )# #F_2 = color(white)(/) 8 1/2# or #17/2#

SOLVE

#A = 73/3 - 53/6 - 17/2#

common denominator

#A = 2/2 xx 73/3 - 53/6 - 17/2 xx 3/3#

#A = 146/6 - 53/6 - 51/6#

#A = (146 - 53 - 51)/6#

#A = 42/6#

#A = 7#

To check our work , #F_1 + F_2 + A# should equal #146/6#

#53/6 + 17/2 + 7#

common denominator

#53/6 + 17/2 xx 3/3 + 7 xx 6/6#

#53/6 + 51/6 + 42/6#

#(53 + 51 + 42)/6#

#146/6#

Yep, we were right. So the attic is #7# feet tall