The perimeter of a rectangular garden is 46. The length is 7 less than 4 times the width. What are the dimensions of the garden?
Dale has $26 to spend at a carnival. If the admission to the carnival is $4 And rides cost $2 each, what is the greatest number of rides Dale can go on?
Let's assume the width of the garden is "w" units.
According to the problem, the length of the garden is 7 less than 4 times the width.
So, the length of the garden is (4w - 7) units.
The formula to calculate the perimeter of a rectangle is: 2 * (length + width).
In this case, the perimeter is given as 46 units.
So, we can set up the equation: 2 * ((4w - 7) + w) = 46.
Simplifying the equation, we get: 2 * (5w - 7) = 46.
Expanding, we have: 10w - 14 = 46.
Adding 14 to both sides, we get: 10w = 60.
Dividing both sides by 10, we get: w = 6.
So, the width of the garden is 6 units.
Substituting this value back into the equation for the length, we have: length = 4w - 7 = 4*6 - 7 = 24 - 7 = 17.
Therefore, the dimensions of the garden are: width = 6 units and length = 17 units.
To find the dimensions of the garden, we can set up a system of equations based on the given information.
Let's assume the width of the garden is represented by W.
According to the problem, the length of the garden is 7 less than 4 times the width. So the length can be represented as (4W - 7).
Since the perimeter of a rectangle is the sum of all its sides, we can set up an equation:
Perimeter = 2(Length + Width)
Given that the perimeter is 46:
46 = 2((4W - 7) + W)
Now, let's solve this equation to find the value of W, which represents the width of the garden.
46 = 2(5W - 7)
Divide both sides by 2:
23 = 5W - 7
Add 7 to both sides:
30 = 5W
Divide both sides by 5:
W = 6
Now that we know the width of the garden is 6, we can substitute this value back into our equation to find the length:
Length = 4W - 7
Length = 4(6) - 7
Length = 24 - 7
Length = 17
Therefore, the dimensions of the garden are 6 units for the width and 17 units for the length.
width ---- x
length ---- 4x - 7
solve for x, then sub into my definition
2x + 2(4x-7) = 46