Mathematics

Question

A publisher needs to send many books to a local book retailer and will send the books in a combination of small and large boxes. Each small box can hold 20 books and each large box can hold 40 books. A total of 8 boxes were sent which can hold 260 books altogether. Determine the number of small boxes sent and the number of large boxes sent.

2 Answer

  • Answer:

    5 large boxes

    3 small boxes

    Step-by-step explanation:

    Create two equations to represent the problem.

    let "a" be the number of small boxes

    let "b" be the number of large boxes

    20a + 40b = 260    This equation shows the numbers of books

    a + b = 8                  This equations shows the number of boxes

    Solve the system of equations (solve for a and b). We can solve using the substitution method.

    Rearrange a + b = 8 to isolate one of the variables.

    a = 8 - b    New equation that represents "a"

    Since we know an equation for "a", we can substitute what "a" equals into the other equation. There will only be one variable in the equation, so we can solve by isolating. Isolate by doing reverse operations.

    Substitute "a" for 8 - b

    20a + 40b = 260

    20(8 - b) + 40b = 260     Distribute 20 over the brackets by multiplying

    160 - 20b + 40b = 260    Collect like terms (numbers with same variables)

    160 + 20b = 260    Start isolating "b". Subtract 160 from both sides

    20b = 260 - 160

    20b = 100    Divide both sides by 20

    b = 5    Number of large boxes

    Substitute "b" for 5 in the simplest equation

    a + b = 8

    a + 5 = 8      Subtract 5 from both sides to isolate "a"

    a = 8 - 5    

    a = 3      Number of small boxes

    Therefore there were 5 large boxes and 3 small boxes sent.

  • Answer:

    s = the number of small boxes

    L = the number of large boxes

    System of Equations:

    25s+40L=250

    s+l=7

    Step-by-step explanation:

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