Abookstore makes a profit of $2.50 on each book they sell, and $0.75 on each magazine they sell. one week, the store sold x books and y magazines, for a weekly profit of $450. the total number of publications sold that week was 260. write and solve a system of equations to determine the number of books and magazine that the bookstore sold that week.

Total books sold=146 books

Total magazines sold=114 magazines

Step-by-step explanation:

Equation 1

Total weekly profit=(Profit for each magazine sold×Number of magazines sold)+(Profit for each book sold×Number of books sold)

where;

Total weekly profit=$450

Profit from each magazine sold=$0.75

Number of magazines sold=y

profit from each book sold=$2.50

Number of books sold=x

Replacing;

450=(0.75×y)+(2.5×x)

0.75y+2.5x=450  Equation 1

Equation 2

Total number of publications sold=Total number of books sold+Total number of magazines sold

where;

Total number of publications sold=260

Total number of books sold=x

Total number of magazines sold=y

x+y=260...   Equation 2

Combine equation 1 and 2 and solve;

1(2.5x+0.75y=450)>>>>>>>>2.5x+0.75y=450

2.5(x+y=260)        >>>>>>>>2.5x+2.5y=650

Subtract equation 1 from 2

(2.5x-2.5x)+(2.5y-0.75y)=(650-450)

1.75y=200

y=200/1.75

y=114

Replacing the value for y in equation 2

x+114=260

x=260-114=146

Total books sold=146 books

Total magazines sold=114 magazines

f(x) has value 150 at x= 0

and 0 at x= 3

so d(f(x))/dt = slope = -150/3 = -50