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?

This problem involves linear equations and can be solved by recognizing that the cost of a cable consists of two components: the fixed cost (the cost of the connectors at both ends), which remains constant regardless of the length of the cable, and the variable cost (the cost per foot of the cable itself), which changes with the length of the cable.
Let's assume that the cost of the connectors is C and the cost per foot of the cable is P. Using the provided information, we can set up two equations based on the total costs of the cables:
Six-foot cable: C + 6P = $15.50 Three-foot cable: C + 3P = $10.25
By subtracting the equation for the three-foot cable from the equation for the six-foot cable, we can find the cost per foot of the cable:
6P - 3P = $15.50 - $10.25 3P = $5.25 P = $1.75
Now we have the cost per foot of the cable, we can find the cost of the connectors by substituting P back into one of the original equations:
C + 3($1.75) = $10.25 C + $5.25 = $10.25 C = $10.25 - $5.25 C = $5.00
Finally, we can calculate the cost of a four-foot cable, which would be C + 4P:
C + 4P = $5.00 + 4($1.75) = $5.00 + $7.00 = $12.00
So, the cost of a four-foot cable would be $12.00.

Answered by IanMckellen | 2024-06-18

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

Answered by apologiabiology | 2024-06-24

The cost of a four-foot cable, considering the cost of the cable per foot and the connectors, is $12.00. This was calculated by first determining the cost per foot of cable and the cost of the connectors from the provided information. By substituting these values, we calculated the cost of the four-foot cable.
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Answered by apologiabiology | 2024-10-31