The credit remaining on a phone card (in dollars) is a liner function of the total calling time made with the card (in minutes) the remaining credit after 30 minutes of calls is $15.20 of the remaining credit after 46 minutes of the call is $12.64 what is the remaining credit after 54 minutes of calls?

$11.36 (11 dollars and 36 cents).

Step-by-step explanation:

This scenario can be written as the linear equation: y = -$0.16x + $20 Where y is the remaining credit, and x is the minutes spend calling.

To find the remaining credit after 54 minutes,

substitute 54 for x and simplify.

So y = -$0.16(54) + $19.60 = -$8.64 + $20.00 =

$20.00 - $8.64 = $11.36.

If you want to solve this problem from scratch, first find the constant rate of money by subtracting 30 minutes (time) over $15.20(total) by 46 minutes over $12.64(total).

Just subtract across, and simplify to get the rate, and then apply that rate between the missing total of 54 minutes and the total of $12.64 dollars for 46 minutes. This is because rate = change quantity/change in time. If that rate is constant as it is in this relationship where the quantity is the amount of anything that is dependent on something, in this case it's money.

So subtract (find the difference) to find the pattern of change between these values in respect to time.

15.20/ 30 - 12.64 / 46 = 2.56 / -16 = 1.28 / -8 = 0.64 / -4 = 0.32 / -2 = 0.16 / -1 = -0.16 [This is the rate decrease in money every minute of a call being made or decrease in remaining credit every minute ].

Now since we know the rate, we can solve the missing factor of the problem by multiplying the rate by the change in time to get the change in quantity.

So : 54 - 46 = 8. 8 × 0.16 = 1.28 [This is the change in quantity from 46 to 54 minutes of calling ].

Therefore, $12.64 [remaining credit from 46 minutes ] - $1.28 [the change of credit from 46 minutes to 54] = $11.36 [remaining credit from 54 minutes].

Also in general, Rate = dependent variable / independent variable.

46

step-by-step explanation:

given

height = 168 cm

formula

height =2.47*f+54.13

solution

168 = 2.47f + 54.13             subtract 54.13 from both sides

168 - 54.13   = 2.47f             combine

113.87 = 2.47f                     divide by 2.47

113.87 / 2.47 = f                   combine

46.1 = f  

answer: 46 cm