Carl has three lengths of cable,56 yard long,14 yard long,and 23 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 shortest pieces, how much more cable would he need?
here hope this helps
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 - yard long,
Cable 2 - yard long,
Cable 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
Taking 1/4 and 2/3
Taking 5/6 and 2/3
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 yards more of cable.
C. After Carl has used 1 yard of cable,how much cable will he have left?
Altogether he has yards of cable.
If he took the 1 cable needed, he would then have 3/4 of a yard leftover.
can you explain it using numbers or sumthin cause I got a work sheet and I try to explain it using numbers
a. To find the two pieces of cable that together make a length at least 1 yard and closest to 1 yard, we need to consider all possible combinations:
- 56 yard long + 14 yard long = 70 yards (exceeds 1 yard)
- 56 yard long + 23 yard long = 79 yards (exceeds 1 yard)
- 14 yard long + 23 yard long = 37 yards (meets the criteria)
Therefore, the two pieces that together make a length at least 1 yard and closest to 1 yard are the 14 yard long and 23 yard long cables.
b. If Carl uses the two shortest pieces, which are 14 yard long and 23 yard long, he would have a total length of 14 + 23 = 37 yards. Since he needs at least 1 yard, he would still need an additional length of 1 - 37 = -36 yards. However, a negative value doesn't make sense in this context, so we can say that he would need an additional length of 0 yards.
To find the two lengths of cable that, when combined, make a length closest to 1 yard, you need to compare all possible combinations. Here's how you can do it:
a. Comparing all combinations:
- Start by comparing the lengths of the cables one by one.
- First, compare the lengths of the 56-yard cable and the 14-yard cable.
- Their sum is 56 + 14 = 70 yards, which is not close to 1 yard.
- Next, compare the lengths of the 56-yard cable and the 23-yard cable.
- Their sum is 56 + 23 = 79 yards, still not close to 1 yard.
- Finally, compare the lengths of the 14-yard cable and the 23-yard cable.
- Their sum is 14 + 23 = 37 yards, which is much closer to 1 yard.
Therefore, the two pieces of cable that, when combined, make a length closest to 1 yard are the 14-yard cable and the 23-yard cable.
b. If Carl uses the two shortest pieces of cable, which are the 14-yard cable and the 23-yard cable, he must calculate how much more cable he would need.
- Add the lengths of the 14-yard and 23-yard cables together:
- 14 + 23 = 37 yards
- Subtract this sum from 1 yard to find the additional cable length needed:
- 1 - 37 = -36 yards
Based on the calculation, using the two shortest pieces of cable will actually result in an excess length of 36 yards, rather than requiring more cable. However, it's important to note that an excess length is not needed in this case since Carl only needs at least 1 yard of cable.