Question

Casey bought 3 books and an 7 CD's and paid $79. Her friend Jane bought a 5 books and 2

Answer 1

Answer:

• book $3
• CD $10

Step-by-step explanation:

We can let b and c represent the cost of a book and the cost of a CD, respectively. Then the purchases can be described by ...

  3b +7c = 79

  5b +2c = 35

Using Cramer's rule to find the solution, we have ...

  b = (7(35)-2(79))/(7(5) -2(3)) = 87/29 = 3

  c = (79(5)-35(3))/29 = 290/29 = 10

The cost of each book was $3; the cost of each CD was $10.

_____

Cramer's rule tells you the solution to ...

  ax +by = c

  dx +ey = g

is ...

  x = (bg -ec)/(bd -ea)

  y = (cd -ga)/(bd -ea) . . . . same denominator

This solution is fully equivalent to using elimination or substitution to solve the problem. Using these formulas effectively "cuts to the chase" without all the intermediate steps. The cross-multiplying pattern of differences is not hard to memorize.