Answer: Elm Street Bookstore has 1,272 books.
Explanation:
Read the problem: Main Street Bookstore has 3,132 books. They have 4 times as many books as Water Street Bookstore. Water Street Bookstore has 489 fewer books than Elm Street Bookstore. How many books does Elm Street Bookstore have?
Highlight facts: Main Street Bookstore has 3,132 books. They have 4 times as many books as Water Street Bookstore. Water Street Bookstore has 489 fewer books than Elm Street Bookstore. How many books does Elm Street Bookstore have?
Draw a picture: I drew a diagram to represent the relationships between the bookstores.
Assign variables: Let x be the number of books that Elm Street Bookstore has, y be the number of books that Water Street Bookstore has, and z be the number of books that Main Street Bookstore has.
Write equations: Based on the facts, I can write three equations:
z = 4y (Main Street Bookstore has 4 times as many books as Water Street Bookstore)
y = x - 489 (Water Street Bookstore has 489 fewer books than Elm Street Bookstore)
z = 3,132 (Main Street Bookstore has 3,132 books)
Solve for x: I can substitute y and z in the first equation with the expressions from the second and third equations:
3,132 = 4(x - 489)
Simplify and solve for x:
3,132 = 4x - 1,956
5,088 = 4x
x = 1,272
Check the answer: I can plug in x = 1,272 in the other equations and see if they are true:
y = x - 489
y = 1,272 - 489
y = 783
z = 4y
z = 4(783)
z = 3,132
All the equations are true, so x = 1,272 is the correct answer.
Hope this helps, and have a great day! =)