Respuesta :
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 = [tex] \frac{36.55}{X} [/tex]
For X < 3.00 ,
Y > [tex] \frac{36.55}{3.00} [/tex] (when X is max, then Y will be min)
⇒ Y > 12.183
and for X > 2.00,
Y < [tex] \frac{36.55}{2.00} [/tex] (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 = [tex] \frac{36.55}{13} = 2.81153846.... [/tex]
If Y= 14 , then X = [tex] \frac{36.55}{14} = 2.6107142... [/tex]
If Y= 15 , then X = [tex] \frac{36.55}{15} = 2.43666666... [/tex]
If Y= 16 , then X = [tex] \frac{36.55}{16} = 2.2843.. [/tex]
If Y= 17 , then X = [tex] \frac{36.55}{17} = 2.15 [/tex]
and if Y = 18 , then X = [tex] \frac{36.55}{18} = 2.0305555... [/tex]
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
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
