Question

The bookstore marked some notepads down from ​$3.00 but still kept the price over ​$2.00. it sold all of them. the total amount of money from the sale of the pads was ​$36.55. how many notepads were​ sold? what was the price of each​ notepad?

Answer 1

Answer: 18 note pads sold and price for each is $2.03

Step-by-step explanation:

This is an algebra problem

denoting k as the price  of each note pads

denoting m as the number of notepads sold

from the problem statement "The bookstore marked some notepads down from ​$3.00 but still kept the price over ​$2.00"

k < $3.00 and k > $2.00

the total amount of money from the sale of the pads was ​$36.55

thus km = $36.55

        m  = $36.55/k

when k < $3.00 when k is maximum, m will be minimum m > $12.18

when k > $2.00 when k is minimum, m will be maximum m < $18.28

if m is the number of notepads sold, the value of m must be a whole number, then minimum value is

thus we iterate to get the minimum

for m = 15

   k = $36.55/15 = $2.44

for m = 16

   k = $36.55/16 = $2.28

for m = 17

   k = $36.55/17 = $2.15

for m = 18

   k = $36.55/18 = $2.03

for m = 19

   k = $36.55/19 = $1.92

Answer 2

The number of notepads sold will be 17 and the price of each notepad is $2.15

Let's assume, the price of each notepad is X and the number of notepads sold is Y

As the price of each notepad is below $3.00 and over $2.00 , that means

X < 3.00 and X > 2.00

As the number of notepads sold is Y, so the total price of all X number of notepads will be : XY

Here it is given that, the total amount of money from the sale of the pads was ​$36.55

So, XY = 36.55

⇒ Y = $\frac{36.55}{X}$

For X < 3.00 ,

Y > $\frac{36.55}{3.00}$ (when X is max, then Y will be min)

⇒ Y > 12.183

and for X > 2.00,

Y < $\frac{36.55}{2.00}$ (when X is min, then Y will be max)

⇒ Y < 18.275

As here Y is the number of notepads sold, so the value of Y must be a whole number. The minimum value of Y will be 13 and maximum value will be 18.

Now we will use hit and trial method

If Y= 13 , then X = $\frac{36.55}{13} = 2.81153846....$

If Y= 14 , then X = $\frac{36.55}{14} = 2.6107142...$

If Y= 15 , then X = $\frac{36.55}{15} = 2.43666666...$

If Y= 16 , then X = $\frac{36.55}{16} = 2.2843..$

If Y= 17 , then X = $\frac{36.55}{17} = 2.15$

and if Y = 18 , then X = $\frac{36.55}{18} = 2.0305555...$

So, for getting XY= 36.55 exactly, the value of X= 2.15 and the value of Y=17.

So, the number of notepads sold will be 17 and the price of each notepad is $2.15