Question

1) Domingo is replacing the baseboards in his home and calculates that he will need 635.8 ft of wood. when he travels to the hardware store he discovers that face boards are sold in 7.5 foot planks how many boards will Domingo need to purchase.2) Faith ,caden and ashlyn entered a race at there school. Faith ran 5 3/5 miles ,caden ran 1.8 miles and ashlyn ran 4 1/3 miles.How much further did ashlyn amd faith run than caden

Answer 1

1) He needs 635.8 ft of wood.

The boards are sold in 7.5 ft, so we can write:

`1\text{ board}=7.5\text{ ft}`

If he needs 635.8 ft, the number of boards is:

`635.8\text{ ft}\cdot\frac{1\text{ board}}{7.5\text{ ft}}\approx84.77\text{ boards}`

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:

`D_F=(5+(3)/(5))-1.8=5+0.6-1.8=5.6-1.8=3.8`

Ashlyn ran 4 1/3 miles, so the difference for her is:

`D_A=(4+(1)/(3))-1.8\approx4+0.3..-1.8=4.3\text{..}-1.8=2.5`

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:

`\begin{gathered} (5+(3)/(5))+(4+(1)/(3))-1.8 \\ (25+3)/(5)+(12+1)/(3)-(9)/(5) \\ (28)/(5)+(13)/(3)-(9)/(5) \\ (19)/(5)+(13)/(3) \\ (19\cdot3+13\cdot5)/(15)=(57+65)/(15)=(122)/(15)=(8\cdot15+2)/(15)=8+(2)/(15) \end{gathered}`

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