Carl has three lengths of cable: [tex]\frac{5}{6}[/tex] yard long, [tex]\frac{1}{4}[/tex] yard long, and [tex]\frac{2}{3}[/tex] yard long. He needs at least one yard of cable. Which two pieces together make a total length that is at least 1 yard and closest to 1 yard?

1/4+2/3 = (3+8)/12 = 11/12 = 0.917 5/6+1/4 = (10+3)/12 = 13/12 = 1.083 5/6+2/3 = (5+4)/6 = 9/6 = 3/2 = 1.5 so, closest to 1 = (1/4+2/3)

Answered by soniaagarwal09 | 2024-06-10

The closest combination of cable lengths adds up to at least 1 yard and is made by combining the lengths of 6 5 ​ yard and 4 1 ​ yard, totaling approximately 1.083 yards. The other combinations exceed 1 yard or fall short. Therefore, the best pair for Carl's needs is the first one.
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Answered by soniaagarwal09 | 2025-01-28