CDs and DVDs Solve by setting up a system of linear equations with 2 variables and 2 unknowns. CDs cost $5.96 more than DVDs at All Bets Are Off Electronics. How much would 6 CDs and 2 DVDs cost if 5 CDs and 2 DVDs cost $127.73?
Accepted Solution
A:
6 CDs and 2 DVDs would cost $147.68.
Let c be the cost of a CD and d be the cost of a DVD.
We know that c = d+5.96.
We also know that 5c+2d = 127.73.
Substituting our value of c from the first equation into the second one, we have 5(d+5.96)+2d = 127.73
Using the distributive property, 5*d+5*5.96+2d = 127.73 5d+29.80+2d = 127.73
Combining like terms, 7d+29.80 = 127.73
Subtract 29.80 from both sides: 7d+29.80-29.80=127.73-29.80 7d = 97.93
Divide both sides by 7: 7d/7 = 97.93/7 d = 13.99 c = d + 5.96 = 13.99+5.96 = 19.95
6 CDs and 2 DVDs would be 6(19.95)+2(13.99) = 147.68