Subtract. (2x4−x2+5x−2)−(−x4+3x3+2x2−1)
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Let p be the prize of a pen and m the prize of a mechanical pencils. If you buy six pens and one mechanical pencil, you spend 6p+m. We know that this equals 9, because you get 1$ change from a 10$ bill.
Similarly, if you buy four pens and two mechanical pencils, you spend 4p+2m, which is 8$, because now you get a $2 change. Put these equation together in a system:
Now, if you multiply the first equation by 2, the system becomes
Subtract the second equation from the first:
Plug this value into the first equation to get
Answer:
x = 14 days
Step-by-step explanation:
To answer the question, find a function that represents the payment mode of plan A and an equation that represents the mode of payment of plan B.
For Plan B the payment is constant every afternoon, $ 11.5 (or 1150 cents) so the equation to represent this form of payment is as follows:
A = 1150x (with units in cents)
This equation represents the line of a line of slope 1150, which passes through point (0,0). Where x is the number of days {1, 2, 3 ....}
In form of payment B, the amount of payment is doubled each day. And the first payment is 2 cents. Therefore this model is represented by an exponential base 2 equation of the form:
Where x represents the number of days, which is always greater than 0 {1, 2, 3, 4 ...}
To know in which day the salary will be approximately the same we equate both equations and we clear x.
A = B
It is a somewhat difficult equation to solve, so I recommend iterating to get a value where the function approaches 0 (when this difference is zero it means that the A and B salaries are the same).
Suppose
x = 13 days
cents
It is not equal to 0.
Let's try with x = 15
cents
Then the value that makes the function zero is between x = 13 and x = 15
Let's try with x = 14
cents = 2.84 $ difference. X = 14 is the whole number where functions A and B are closer together (the salary is approximately the same). Therefore the answer is
x = 14 days