I am terrible at word problems. How do I work this?
A large park is to be built in the shape of a rectangle. The length is to be 5 m shorter than three times the width. The perimeter of the park is to be 750 m. What will be the length and
width of the park?
The main idea is to "translate" the English into math
let the width be x
"The length is to be 5 m shorter than three times the width."
length = 3x-5
so now we know the width is x
and the length is 3x-5
"The length is to be 5 m shorter than three times the width."
Isn't perimeter the sum of all the sides ? So ...
x + x + 3x-5 + 3x-5 = 750
now you have an easy equation to solve, let me know what you got.
8x+(-10)=750
8x=760
x=95
y=95(3)=285
w=95
L=285
To solve this word problem, we can break it down into steps:
Step 1: Assign variables.
Let's assign variables to the length and width of the park to make it easier to work with. Let's call the width "x" meters. Then, the length can be expressed as "3x - 5" meters.
Step 2: Set up the equation.
The perimeter of a rectangle is found by adding up all its sides. In this case, the perimeter is given to be 750 m. So, we can set up the equation:
Perimeter = 2(length + width) = 750
Step 3: Substitute the values.
Substitute the expressions for length and width into the equation we just set up:
2(3x - 5 + x) = 750
Step 4: Simplify and solve.
Distribute the 2 to the terms inside the parentheses:
2(4x - 5) = 750
Now, simplify the equation by multiplying:
8x - 10 = 750
Next, isolate the variable by adding 10 to both sides of the equation:
8x = 760
Finally, solve for x by dividing both sides of the equation by 8:
x = 95
Step 5: Find the length.
We know that the length is 5 meters less than three times the width. So, substitute the value of x we found into the expression:
3x - 5 = 3(95) - 5 = 285 - 5 = 280
Therefore, the length of the park is 280 meters and the width is 95 meters.