Question

Connecting a DVD player to a television set requires a cable with special connectors at both ends. You buy a six-foot cable for $15.50 and a three-foot cable for $10.25. Assuming that the cost of a cable is the sum of the cost of the two connectors and the cost of the cable itself, what is the cost of a four-foot cable?

Answer 1

So a 3 foot cable is10.25
a 6foot cable is 15.50
so
x=cost per foot
y=cost of special connectors
3x+y=10.25
6x+y=15.50
make first equation negative and add to the first
3x=5.25
divide both sides by 3
1.75=x
so it costs 1.75 for a foot of cable

subtitue into first equation
3(1.75)+y=10.25
5.25+y=10.25
subtract 5.25 from both sides
y=5 dollars=cost of special so
4x+y=4(1.75)+5=7+5=$12

so the cost of a 4 foot cable is $12