Question 615961
c = number of cd's that were bought.
d = the number of dvds that were bought.
6c + 4d = 77.80
11c + 14d = 192.25
use one of the equations to solve for d in terms of c.
then use that value for d in the other equation.
from the first equation, you get:
6c + 4d = 77.80
subtract 6c from both sides of the equation to get:
4d = 77.80 - 6c
divide both sides of the equation by 4 to get:
d = (77.80 - 6c) / 4
substitute this equation for d in the other equation to get:
11c + 14d = 192.25 becomes:
11c + 14*((77.80-6c)/4) = 192.25
simplify by removing parentheses to get:
11c + (1089.2 - 84c)/4 = 192.25
multiply both sides of the equation by 4 to get:
44c + 1089.2 - 84c = 769
subtract 1089.2 from both sides of the equation to get:
44c - 84c = 769 - 1089.2
simplify to get:
-40c = -320.2
divide both sides of the equation by -40 to get:
c = 8.005
take the first original equation and replace c with 8.005 and solve for d.
the first original equation is:
6c + 4d = 77.80
replace c with 8.005 to get:
6*8.005 + 4d = 77.80
simplify to get:
48.03 + 4d = 77.80
subtract 48.03 from both sides of the equation to get:
4d = 77.80 - 48.03
simplify to get:
4d = 29.77
divide both sides of the equation by 4 to get:
d = 7.4425
you have:
c = 8.005
d = 7.4425
substitute these values for c and d in the second original equation.
11c + 14d = 192.25 becomes:
11*8.005 + 14*74425 = 192.25
simplify to get:
88.055 + 104.195 = 192.25 which becomes:
192.25 = 192.25 confirming the values for c and d are correct.