Question

The perimeter of a flag is 154 in. The length is 3 in greater than the width. Let L= the length and W=the width. Write and solve a system of equations to model the situation.

a) L + W = 154
L - W = 3

b) 2L + 2W = 154
L - W = 3

c) L + W = 154
L + 3 = W

d) 2L + 2W = 154
L + 3 = W

Answer 1

The correct system of equations to represent the given situation for the flag's dimensions is 2L + 2W = 154 and L = W + 3. By solving this system, we discover that the width (W) is 37 inches, and the length (L) is 40 inches.

Step-by-step explanation:

To find the correct system of equations to model the situation, we must consider that the perimeter (P) of a rectangle is calculated by adding together twice the length (L) and twice the width (W). Since the perimeter is given as 154 inches, our first equation becomes 2L + 2W = 154. Next, since the length is 3 inches greater than the width, we have L = W + 3.

The correct system of equations is thus:

2L + 2W = 154

L = W + 3

To solve this system, we can first solve the second equation for L, yielding L = W + 3. Substituting this into the first equation results in 2(W + 3) + 2W = 154, which simplifies to 2W + 6 + 2W = 154. Combining like terms gives us 4W + 6 = 154. Subtracting 6 from both sides results in 4W = 148. Finally, dividing by 4, we find that W = 37. Now that we have W, plug it back into L = W + 3 to find L = 40.