Answer:
A- 5/6 and 1/4
B- 1/12
C- 3/4
Step-by-step explanation:
Given : Carl has three lengths of cable,
Cable 1 - [tex]\frac{5}{6}[/tex] yard long,
Cable 2 - [tex]\frac{1}{4}[/tex] yard long,
Cable 3 - [tex]\frac{2}{3}[/tex] yard long
He needs at least 1 yard of cable.
A. Which two pieces together make a length at least 1 yard and closest to 1 yard?
We can form possible piece together
Taking 5/6 and 1/4
[tex]\frac{5}{6} +\frac{1}{4}= \frac{20+6}{24}=\frac{26}{24}=1.08[/tex]
Taking 1/4 and 2/3
[tex]\frac{1}{4} +\frac{2}{3}= \frac{3+8}{12}=\frac{11}{12}=0.91[/tex]
Taking 5/6 and 2/3
[tex]\frac{5}{6} +\frac{2}{3}= \frac{15+12}{18}=\frac{27}{18}=1.5[/tex]
Length at least 1 yard and closest to 1 yard is the 5/6 yard and the 1/4 yard together.
B. If Carl uses the two short pieces,how much more cable would be need?
The two short pieces 1/4 and 2/3 makes 11/12 of a yard,
So, he would need [tex]1-\frac{11}{12}= \frac{12-11}{12}=\frac{1}{12}[/tex] yards more of cable.
C. After Carl has used 1 yard of cable,how much cable will he have left?
Altogether he has [tex]\frac{5}{6} +\frac{1}{4}+\frac{2}{3}=\frac{126}{72}=1and\frac{3}{4}[/tex] yards of cable.
If he took the 1 cable needed, he would then have 3/4 of a yard leftover.