[SPLIT] A company installs underground cable for \$500 for 1st 50

Simplificatation, evaluation, linear equations, linear graphs, linear inequalities, basic word problems, etc.
starr
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[SPLIT] A company installs underground cable for \$500 for 1st 50

hello!!!

I have a word problem of which I do not understand.

A company installs underground cable at a cost of \$500 for the first 50ft and \$5 for each
additional foot thereafter. Express the cost C as a function of the length L of underground cable if L >50ft

do anyone have a master technique that I can use???

stapel_eliz
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When in doubt, try plugging in numbers. See what you do with the actual numbers, and then do the same with the letters.

If they install 50 feet, how much do they charge?

If they install 51 feet, how much do they charge?

If they install 55 feet, how much do they charge?

If they install 60 feet, how much do they charge?

Do you see a pattern? If so, then:

If they install "L" feet, how much do they charge?

Eliz.

starr
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Re: [SPLIT] A company installs underground cable for \$500 for 1s

hello eliz!!!!

I see your point!!! my problem is I am not sure how to set up the fuction.

stapel_eliz
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"Express the cost C as a function of the length L" means to write the formula using function notation: C(L) = (something with L in it).

So look at the pattern you found, plug "L" into this pattern (in place of the numbers you'd used before), and set it equal to "C(L)".

Eliz.

starr
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Re: [SPLIT] A company installs underground cable for \$500 for 1s

hello eliz!!!

the calculation I came up with is

c=5l +500

I dont think that's quite right

stapel_eliz
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the calculation I came up with is

c=5l +500
How did you arrive at this formula?

You plugged in various numbers, such as those suggested earlier, and did the computations, paying close attention to your steps and reasoning:

. . . . .L = 50, so extra length is 50 - 50 = 0:
. . . . .C = 500 + 5(0) = 500 + 5(50 - 50)

. . . . .L = 51, so extra length is 51 - 50 = 1:
. . . . .C = 500 + 5(1) = 500 + 5(51 - 50)

. . . . .L = 52, so extra length is 52 - 50 = 2:
. . . . .C = 500 + 5(2) = 500 + 5(52 - 50)

. . . . .L = 55, so extra length is 55 - 50 = 5:
. . . . .C = 500 + 5(5) = 500 + 5(55 - 50)

. . . . .L = 60, so extra length is 60 - 50 = 10:
. . . . .C = 500 + 5(10) = 500 + 5(60 - 50)

...and so forth. What pattern did you see?

Eliz.

starr
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Re: [SPLIT] A company installs underground cable for \$500 for 1s

my reasoning for the formula was simple. 500for the first 50 ft and 5 times for the extra length.
I see a pattern of which as the length increase by five. Is that what you referring to???

starr
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Re: [SPLIT] A company installs underground cable for \$500 for 1s

at some point L has to be greater than 50

DAiv
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Re: [SPLIT] A company installs underground cable for \$500 for 1s

C = 5L + 500

My reasoning for the formula was simple. 500 for the first 50 ft and 5 times for the extra length.
Remember, 'L' is the whole length, not the extra length.

DAiv