a roll of carpet 9 ft wide is 30 ft longer than a roll of carpet 15 ft wide. both rolls have the same area. make a sketch and find the dimensions of each.
first represent unknowns with variables:
let x = length of the second carpet
let x+30 = length of first carpet.
since Area=length*width, and they have the same area,
Area = 9*(x+30) = 15*x
9(x+30) = 15x
now solve for x. then substitute this to x+30 to get length of first carpet.
let me see your work. :)
15 by 45; 9 by 75
X=45
15 by 45 and 9 by 75
To solve this problem, we can start by drawing a sketch to better visualize the situation. Let's represent the roll of carpet that is 9 ft wide with the variable "x" and the roll of carpet that is 15 ft wide with the variable "y".
Now, let's list the information given in the problem:
1. The roll of carpet that is 9 ft wide is 30 ft longer than the roll of carpet that is 15 ft wide.
2. Both rolls have the same area.
With this information, we can set up two equations based on the given conditions.
Equation 1: Length of the 9 ft wide roll = Length of the 15 ft wide roll + 30 ft
Equation 2: Area of the 9 ft wide roll = Area of the 15 ft wide roll
Let's solve the problem step by step.
Step 1: Express the width of the rolls as a variable. Let's represent the width of the 9 ft wide roll as "x" and the width of the 15 ft wide roll as "y".
Step 2: Write down Equation 1:
Length of x = Length of y + 30
Step 3: Write down Equation 2:
Length of x * Width of x = Length of y * Width of y
Step 4: Substitute the width values into Equation 2:
(x) * (9) = (y) * (15)
Step 5: Simplify Equation 2:
9x = 15y
Step 6: Solve Equation 1 for the length of y:
Length of y = Length of x - 30
Step 7: Substitute the length of y into Equation 2:
(x) * (9) = (Length of x - 30) * (15)
Step 8: Expand Equation 7:
9x = 15Length of x - 450
Step 9: Combine like terms and move all terms to one side:
6Length of x = 450
Step 10: Solve for Length of x:
Length of x = 450 / 6 = 75 ft
Step 11: Substitute the Length of x in Equation 1 to solve for Length of y:
Length of y = 75 ft - 30 ft = 45 ft
So, the dimensions of the 9 ft wide roll are 75 ft long and 9 ft wide, while the dimensions of the 15 ft wide roll are 45 ft long and 15 ft wide.