Dan is cutting 4.75 foot legths of twine from a 240 foot spool of twine. He needs to cut 42 lengths, and says that 40.5 feet of twine will remain. Show that this is reasonable.
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4.75 * 42 = 199.5 feet
Or to estimate -- 40 * 5 = 200
To show that it is reasonable for 40.5 feet of twine to remain after cutting 42 lengths of 4.75-foot twine from a 240-foot spool, we can calculate the total length of twine used for cutting 42 lengths and compare it with the initial length of the spool.
First, calculate the length of twine used for cutting 42 lengths:
42 lengths * 4.75 feet/length = 199.5 feet
Next, subtract the length of twine used from the initial spool length:
240 feet - 199.5 feet = 40.5 feet
Therefore, it is reasonable for 40.5 feet of twine to remain after cutting 42 lengths of 4.75-foot twine from a 240-foot spool.
To show that it is reasonable for 40.5 feet of twine to remain after cutting 42 lengths of 4.75 feet each from a 240-foot spool, we can do the following calculation:
1. Determine the total length of twine used for cutting 42 lengths:
42 lengths * 4.75 feet/length = 199.5 feet
2. Calculate the remaining length of twine:
240 feet - 199.5 feet = 40.5 feet
So, according to the calculations, 40.5 feet of twine should remain after cutting 42 lengths of 4.75 feet each from a 240-foot spool.
It is reasonable because the total length of twine used for cutting 42 lengths is less than the initial spool length, and the remaining length of twine matches the calculation.