Let's call the two numbers a and b. So we know that the difference of the two numbers is 36:
a - b = 36
And we know that their sum is 286:
a + b = 286
We can use either of these equations to solve for one of the variables in terms of the other variable. Let's use the first and solve for a:
a - b = 36
a = 36 + b
Now we plug this into the other equation and solve for b there:
(36 + b) + b = 286
36 + 2b = 286
2b = 250
b = 125
Answer: length = 19 inches and width = 8 inches
Step-by-step explanation: To solve this problem, our first task is to set up variables.
Since the length of the rectangle is 5 inches less than 3 times its width, we can set up variables to represent this.
Variables
X ⇒ width
3x - 5 ⇒ length
To help set up our equation, I will draw a picture of the rectangle labeling the widths X and the lengths 3x - 5.
Going back to the original problem, the second sentence states that the perimeter of he rectangle is 54 inches. Remember that the perimeter is the distance around the rectangle.
Based on the picture I provided, our equation will read as followed.
X + X + (3x -5) + (3x - 5) = 54
8x - 10 = 54 ← simplify on the left side of the equation
+10 +10 ← add 10 on both sides
8x = 64
÷8 ÷8
X = 8
Therefore, the width of our rectangle is 8 inches and the length of our rectangle is (3 x 8) - 5 or 19.
Answer:
D would be the correct answer.
As you can see in the second equation, y is already isolated. So, we can substitute it into the first equation, to solve for x.
Let me know if this helps!
#4
(5/4)*5= (25/4)=6 1/4 miles per hr
#5
(40/$62) = (x/$128.65)
x = 83