Question

QUICK PLEASE HELPPPPPPPPPPPP

Answer 1

Answer: 16

=====================================================

Step-by-step explanation:

Set the expression equal to 100 and get everything to one side

`d^2 - 12d + 45 = 100\\\\d^2 - 12d + 45 - 100 = 0\\\\d^2 - 12d - 55 = 0\\\\`

Now use the quadratic formula. We'll plug in a = 1, b = -12, c = -55.

`\ d = (-b\pm√(b^2-4ac))/(2a)\\\\\ d = (-(-12)\pm√((-12)^2-4(1)(-55)))/(2(1))\\\\\ d = (12\pm√(364))/(2)\\\\\ d \approx (12\pm19.07878403)/(2)\\\\\ d \approx (12+19.07878403)/(2)\ \text{ or } \ d \approx (12-19.07878403)/(2)\\\\\ d \approx (31.07878403)/(2)\ \text{ or } \ d \approx (-7.07878401)/(2)\\\\\ d \approx 15.53939201\ \text{ or } \ d \approx -3.53939201\\\\d \approx 15.54 \ \text{ or } \ d \approx -3.54`

We'll ignore the negative d value as we can't have a negative number of days.

This means d = 15.54 is the only approximate solution we'll consider.

If we plugged in d = 15, then,

d^2 - 12d + 45

(15)^2 - 12(15) + 45

90

This tells us that 90 masks were sold on day d = 15.

Now try d = 16

d^2 - 12d + 45

(16)^2 - 12(16) + 45

109

We see that 109 masks were sold on day d = 16. Somewhere between those days, 100 masks were sold. At the end of the 15th day, we got to 90. So in the middle of day 16 is when we reach the exact 100 mark we're after.

In short, we would round d = 15.54 up to d = 16 so that we clear the hurdle.

In other words, if you rounded d = 15.54 to d = 15, then you'd be 10 masks short of the goal. Besides, 15.54 rounds to 16 when rounding to the nearest whole number.