Final answer:
The width of Darrin's yard is approximately 47 feet and the length is 134 feet. These dimensions satisfy the conditions that the length is 7 feet less than three times the width, and that 318 feet of garland covers three sides of the yard.
Step-by-step explanation:
The student's question involves solving a system of linear equations to determine the length and width of Darrin's front yard. Since we know Darrin is hanging 318 feet of holiday garland around three sides of the fencing, the perimeter we need to consider is those three sides combined. We can set up two equations to represent this scenario, with L representing the length and W representing the width of the yard.
The problem states the length is 7 feet less than three times the width, which gives us the equation L = 3W - 7. Additionally, we know that the total length of the garland hung on three sides of the yard is 318 feet, leading to the equation 2L + W = 318 since the garland covers two lengths and one width of the fence. Substituting the first equation into the second gives us: 2(3W - 7) + W = 318. Simplifying, we get 6W - 14 + W = 318, and further simplification yields 7W - 14 = 318. Adding 14 to both sides gives 7W = 332, and dividing by 7 gives us W = 47.4286, which rounds approximately to W = 47 feet for the width. Using this width to find the length, we have L = 3(47) - 7 = 141 - 7 = 134 feet.