System of equations question

Question

Several books are on sale at a bookstore. Some of these books cost $3 and others cost $5. One day last week, 80 of these books were sold. The total amount of the sales was $300. How many of each type were sold? Use a system of equations to answer the questions.

Answer 1

Hi Angel. In order to answer this question, we should first:

let b represent the books that cost 3 dollars

let o represent the other books that cost 5 dollars

Now we can set up our system of equations.

The first equation represents the total number of books.

b+o=80

The second equation represents the total price of the books

3b+5o= $300

We must isolate one variable in the first equation, or move the other variable to the right side of the equation. If we choose to find b, we must move the o variable to the right side of the equation.

b+o=80

b=80-o

We now know that b=80-o. We can plug this into the second equation as the value of b and solve for o.

3b+5o=$300

3(80-o)+5o=$300

240-3o+5o=$300; distributed 3 or multiplied each term in the parentheses by 3

240+2o=$300;combined like terms, which were -3o and 5o

2o= 60; subtracted 240 from both sides of the equation

o=30

We now know that o is equal to 30. we can now find the value of b by plugging this value into the first equation and solving for b.

b+30=80

b = 50; subtracted 30 from both sides

If you have any questions, or want to schedule a lesson with me, please do not hesitate to contact me through Wyzant.

Answer 2

F + T = 80, where F is the # of $5 books and T = # of $3 books

5F + 3T=300

F=80-T

Substitute

5(80-T)+3T=300

400-5T+3T=300

You take it from here.