To answer this question, we need to take into account that we have here operations with mixed fractions. Then, we can pose the operations as follows:
1. We have a total of 68 and 3/4 acres.
2. How many acres of wooded land will remain if we subtract 4/5 acres from the total?
Then, we can proceed as follows:
[tex]68\frac{3}{4}=68+\frac{3}{4}=\frac{68\cdot4+1\cdot3}{4}=\frac{272+3}{4}=\frac{275}{4}[/tex]Thus, we have that 4/5 from the total is:
[tex]\frac{275}{4}\cdot\frac{4}{5}=\frac{1100}{20}=\frac{110}{2}=55[/tex]We have that 55 acres are cleared for development. We have at the beginning 275/4 acres (68 plus 3/4 acres). Now, we need to subtract 55 acres from the latter. Then, we have:
[tex]\frac{275}{4}-55=\frac{275\cdot1-55\cdot4}{4}=\frac{275-220}{4}=\frac{55}{4}=\frac{52}{4}+\frac{3}{4}=13+\frac{3}{4}=13\frac{3}{4}[/tex]Therefore, there will remain 13 and 3/4 of acres of wooded land (first option).
(As we can see this last value is 1/5 of the total acres of the wooded piece of land.)
