ABC Bookstore sells packages of books that include both new and used
books. New books cost $16 and used books cost $7. The bookstore wants to
sell packages that have 45 books total, and the store charges $450 for each
package. How many new and used books will be in each package?
O
A. 30 new, 15 used
O
B. 7 new, 16 used
O
O
C. 15 new, 30 used
D. 16 new, 7 used

The answer is c) 15 new books and 30 used books

Step-by-step explanation:

What we need to do to answer this question is create two expressions using variables x and y then combine the equations to solve for one variable, then use this answer to find the value for the second variable.

To do this we must first define our variables: I chose to let x represent the number of new books, and I let y represent the number of used books

Next using these variables we must create two equations, one that equals the total number of books in the package, and another that equals the total cost of the package.

For total number of books 45= x + y (lets call this equation 1)

For total cost 450= 16x + 7y (lets call this equation 2)

Next we need to rearrange so that both equations equal a common variable, for this I chose y

*Remember when moving a term from one side of the equal sign to the other we must switch the sign of the term

For equation 1:

45 = x + y

45 - x =y

y= 45-x

For equation 2:

450 = 16x +7y

450 - 16x = 7y

450/7 -16x/7 =y

Next we let one equation equal the other, we can do this since the y variable in each equation has the same value

450/7 - 16x/7 = 45 - x

Now we need to rearrange this equation so that the terms with x are on the same side, and the constants (terms without x) are on the other side

x- 16x/7 = 45 - 450/7

Now we combine our like terms (terms with the same variable)

9x/7 = 135/7

Since both sides are divided by 7 we can cancel them out to get

9x = 135

Now we solve for x, we can do this by dividing both sides by 9 to get x on its own

x= 135/9

x=15

Using this value for x we can now solve for y

You can chose either equation 1 or 2 from earlier, I chose equation 1 because it is easier to work with

y = 45 - x

y = 45 - 15

y= 30

So our final answer is each package with contain 15 new books and 30 used books

Hope this helps :)

check above link.

graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;