Respuesta :
1) He needs 635.8 ft of wood.
The boards are sold in 7.5 ft, so we can write:
[tex]1\text{ board}=7.5\text{ ft}[/tex]If he needs 635.8 ft, the number of boards is:
[tex]635.8\text{ ft}\cdot\frac{1\text{ board}}{7.5\text{ ft}}\approx84.77\text{ boards}[/tex]He needs to purchase 85 boards.
2) Caden ran only 1.8 miles.
Faith ran 5 3/5 miles, so the difference with Caden is:
[tex]D_F=(5+\frac{3}{5})-1.8=5+0.6-1.8=5.6-1.8=3.8[/tex]Ashlyn ran 4 1/3 miles, so the difference for her is:
[tex]D_A=(4+\frac{1}{3})-1.8\approx4+0.3..-1.8=4.3\text{..}-1.8=2.5[/tex]Faith ran 3.8 more miles than Caden.
Ashley ran 2.5 miles more than Caden.
If we add Faith miles and Ashley miles, adn subtract what Caden ran, we get:
[tex]\begin{gathered} (5+\frac{3}{5})+(4+\frac{1}{3})-1.8 \\ \frac{25+3}{5}+\frac{12+1}{3}-\frac{9}{5} \\ \frac{28}{5}+\frac{13}{3}-\frac{9}{5} \\ \frac{19}{5}+\frac{13}{3} \\ \frac{19\cdot3+13\cdot5}{15}=\frac{57+65}{15}=\frac{122}{15}=\frac{8\cdot15+2}{15}=8+\frac{2}{15} \end{gathered}[/tex]The answer is 8 2/15.
NOTE: in the last step, in order to transform 122/15 in a mixed number, I divide 122 by 15 and see that it was 8.13... Then, the whole part of the mixed number had to be 8. 8 expressed in 1/15 fraction is 8=120/5, so the remainder was 2/15. Then 122/15 = 8 2/15
