Math
posted by Jen .
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?

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+0m = 8
0+c+h+m = 61
0+ch+0 = 15
subtract #2 from #3 and #4
a+0+h+m = 72
0+c+0m = 8
0+0+h+2m = 53
0+0h+m = 23
add #3 to #4
a+0+h+m = 72
0+c+0m = 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. 
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
Similar Questions

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? 
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? 
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? 
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 … 
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 … 
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? 
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? 
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? 
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 … 
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 …