A student bought x books at $8.50 each and y books at $12.50 each. The total cost of the seven books he bought was $17.50. How many of each book did he buy?

Answer 1

there's a mistake in the problem somewhere, a typo maybe.

x+y = 7

8.50x + 12.50y = 175.00

the only solution with these number is a negative number of books or fractional books

for 7 books, these are the possibilities

x y total cost

0 7 87.50

1 6 83.50

2 5 79.50

3 4 75.50

4 3 71.50

5 2 67.50

6 1 63.50

7 0 59,50

never near $175

maybe the problem should have read $75.50 instead of $175? then 3 $8.50 books and 4 $12.50 books sum to $75.,50

but if you want to try to solve the problem as given, then:

x+y + 7

8.5x + 12.5y = 59.5

8.5x + 12.5y = 175

8.5x + 8.5y = 59.5

subtract to get

4y = 115.50

y= 28.875 books costing $12.50 each

and x = 7- 28.985 = -21.985 $8.50 books

that's a negative number of $8.50 books

about 29 $12.50 books and negative 22 $8.50 books

29-22 = 7 total books

8,5(-22) + 12.5(29) = -187 + 362.5 = 175.5

negative 22 books might mean you sold 22 books and bought 29 books. -22+29 = net 7 bought