The credit remaining on a phone card (in dollars) is a linear function of the total calling time made with the card (in minutes). the remaining credit after 39 minutes of calls is $25.32, and the remaining credit after 57 minutes of calls is $23.16. what is the remaining credit after 60 minutes of calls?

One way to write a linear equation is the formula y = mx + b where m is the slope of the function and b is the y-intercept. For this reason, it is known as slope-intercept form.

The slope os calculated via the formula . Lets calculate the slope of the equation first.

So the slope is -0.12. This means for every minute of time used, $0.12 of credit is used. Next, lets plug in the value for m, and the values of an x and y point to find b.

y = 0.12x + b

23.16 = -0.12(57) + b

23.16 = -6.84 + b

30 = b

So, our final equation is y = -0.12x + 30.

Finally, we can use this equation to find the answer to the last part by plugging the value into x.

y = -0.12(60) + 30

y = -7.2 + 30

y = 22.8

So when 60 minutes have been used, there will be $22.80 worth of credit left.

step-by-step explanation:

30% of $420 is 0.30($420) = $126 and $420 + $126 = $546.

or, 130% of $420 is 1.3($420) = $546.

notice that this is not the $600 original list price with which we started.

why doesn't this work?

the method does not work because 30% of $420 is not the same amount as the 30% of $600. it may seem obvious when stated this way, but it is a very common error made on problems of this type. we cannot just use the same percent and get back to the original amount because we are taking that percent of a different value.

to work problems of this type correctly, it is generally best to write an equation for the situation and then solve.

example: since (100% – 30%)(original price) = (sale price)

70% of the   (original price) is $420.

0.7x   = 420

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x = 600

the original cost was $600.

we may also solve this problem using the two-step method. working the problem in two steps requires us to use more algebra skills. we have to know that x = 1x (identity property of multiplicationtext annotation indicator) and that 1x – 0.3x = 0.7x (subtracting like terms). then we solve the problem as follows:

(original price) – 30%(original price) = sale price

x – 0.3x = 420

0.7x = $420

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x = 600

the original cost was $600.  

note that with both of the above methods we do obtain the correct original amount.

example: after a 5% pay raise, hermione is earning $22,680 per year. what was she earning before the pay raise?

105% of (original salary) = current salary

1.05x = 22,680

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x = 21,600

hermione earned $21,600 per year before the pay raise.

this is an example so maybe you will get how to at least do it!

it shoild be o

step-by-step explanation: