Question

Carl has three lengths of cable,5/6/ yard long,1/4 yard long, and 2/3 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?
B. If Carl uses the two short pieces,how much more cable would be need?
C. After Carl has used 1 yard of cable,how much cable will he have left?explain your answer

Answer 1

a. the 5/6 yard and the 1/4 yard
b. the two short pieces makes 11/12 of a yard, he would need 1/12 yards more of cable.
c. altogether he has 1 and 3/4 yards of cable. If he took the 1 cable needed, he would then have 3/4 of a yard leftover.

Answer 2

A- 5/6 and 1/4

B- 1/12

C- 3/4

Explanation:

Given : Carl has three lengths of cable,

Cable 1 -
`(5)/(6)` yard long,

Cable 2 -
`(1)/(4)` yard long,

Cable 3 -
`(2)/(3)` 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

`(5)/(6) +(1)/(4)= (20+6)/(24)=(26)/(24)=1.08`

Taking 1/4 and 2/3

`(1)/(4) +(2)/(3)= (3+8)/(12)=(11)/(12)=0.91`

Taking 5/6 and 2/3

`(5)/(6) +(2)/(3)= (15+12)/(18)=(27)/(18)=1.5`

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
`1-(11)/(12)= (12-11)/(12)=(1)/(12)` yards more of cable.

C. After Carl has used 1 yard of cable,how much cable will he have left?

Altogether he has
`(5)/(6) +(1)/(4)+(2)/(3)=(126)/(72)=1and(3)/(4)` yards of cable.

If he took the 1 cable needed, he would then have 3/4 of a yard leftover.