Math

posted by .

First student bought art, math and history books for $72. a+m+h=72
Second student bought art, chemistry and history books for $80. a+c+h=80
Third student bought chemistry, math and history books for $61. c+m+h=61
Fourth student bought art, math and chemistry books for $57. a+m+c=57
How much does each book cost?
How would you do this without guess and check?

  • Math -

    You have 4 equations in 4 unknowns, so use elimination or substitution. For example,

    a+0+h+m = 72
    a+c+h+0 = 80
    0+c+h+m = 61
    a+c+0+m = 57

    subtract #1 from #2 and #4
    a+0+h+m = 72
    0+c+0-m = 8
    0+c+h+m = 61
    0+c-h+0 = -15

    subtract #2 from #3 and #4
    a+0+h+m = 72
    0+c+0-m = 8
    0+0+h+2m = 53
    0+0-h+m = -23

    add #3 to #4
    a+0+h+m = 72
    0+c+0-m = 8
    0+0+h+2m = 53
    0+0+0+3m = 30

    so, m=10
    use that to fill in the other values, working your way up the rows.

  • Math -

    subtracting 1st from 2nd ... c - m = 8
    ... c = m + 8

    substitute into 3rd ... 2m + h = 53 (A)

    substitute into 4th ... 2m + a = 49 (B)

    subtracting ... h - a = 4

    adding to 1st ... 2h + m = 76
    ... multiply by 2 ... 4h + 2m = 152
    ... subtract A ... 3h = 99 ... h = 33


    substitute to find m , c , and a

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math

    Mickey bought 3 books from the bargain bin at his school's book fair and paid six dollars. If buying books from the bargain bin follows a direct variation, how much did his sister pay for the 4 books she bought?
  2. Maths (Linear Equation)

    Nine books are to be bought by a student. Some cost $6.00 each and the remainder cost $6.50 each. If the total amount spent was $56, how many of each book are bought?
  3. Math

    Nine books are to be bought by a student. Some cost $6.00 each and the remainder cost $6.50 each. If the total amount spent was $56, how many of each book are bought?
  4. Math

    The number of library books in a school increased by 20% after it bought new books in may. The number increased by another 20% after a bookstore donated 300 books in June. Find the number of books in the library before it bought new …
  5. Math

    The number of library books in a school increased by 20% after it bought new books in may. The number increased by another 20% after a bookstore donated 300 books in June. Find the number of books in the library before it bought new …
  6. 3rd grade math

    There are 30 books in a bookcase. The books in the bookcase are all poetry, history, and art books. Ten of the books are art books. There are 6 fewer poetry books than history books. How many poetry books are in the bookcase?
  7. math

    A student has 4 English books,3 math books,and 5 history books.In how many ways can these books be arranged on a shelf if the books in same subjects must be kept together?
  8. math

    Ralph bought 4 books for k dollars each. Iris bought 5 books for k dollars each. If together they spend 90 dollars, how much is each book?
  9. math

    The no of library books in a school increased by 20% after it bought new books in May , the number increased by another 20% after a book store donated 300 books in June - Find the no of books in library before it bought new books in …
  10. Math

    the number of library books in a school increased by 20% after it bought new books in May , the number increased by another 20% after a bookstore donated 300 books in June - Find the number of books in the library before it bought …

More Similar Questions