Question

A plumber can be paid according to the following schemes:In the first scheme he will be paid rupees 500 plus rupees 70 per hour,and in the second scheme he will paid rupees 120 per hour.If he works x hours,then for what value of x does the first scheme give better wages?
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Answer 1

$\textbf {Hey there, here is the solution.}$

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Given that x is the number of hours work.

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STEP 1: Form equations:

First scheme:

Under the first scheme, the plumber gets a fixed wage of Rs 500 regardless of the number of hours he works. On top of that, he is paid Rs 70 for every hour he works. So we add 500 to the number of Rs 70 he will get depending on the number of hours he works.

Wages = 500 + 70x

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Second scheme:

Under the second scheme, the plumber is not given any fixed amount. However, he is paid more per hour compared to the first scheme. He is paid Rs 120 for every hour he works.

Wages = 120x

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STEP 2: Find x when first scheme gives a better wage:

For the first scheme to be a better deal, the total earning gotten from it must be more than the earning he can get from the second term.

500 + 70x > 120x

500 > 120x - 70x

500 > 50x

50x < 500

x < 500 ÷ 50

x < 10

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Answer; First scheme will give a better wage if he works less than 10 hours.

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$\textbf {Cheers}$

Answer 2

Answer:

Here is your answer to the question.

Step-by-step explanation:

I scheme with x hr  500 + (x - 1) 70 = 500 + 70x – 70  = 430 + 70x  II scheme with x hours  120x  Here I > II  ⇒ 430 + 70x > 120x  ⇒ 120x – 70x < 430  50x < 430 50x/50 < 430/50 x < 8.6 (i.e.) when x is less than 9 hrs the first scheme gives better wages.