a rope 25 feet long is cute into 3 peices. The first peice is 2x feet long, the second peice is 5x feet long, and the third piece is 4 feet long.
We can solve this problem by setting up an equation and solving for x.
According to the information given, the first piece is 2x feet long, the second piece is 5x feet long, and the third piece is 4 feet long. We also know that the total length of the rope is 25 feet.
Therefore, we can write the equation:
2x + 5x + 4 = 25
Combining like terms, we get:
7x + 4 = 25
Subtracting 4 from both sides, we have:
7x = 21
Finally, dividing both sides by 7, we get the value of x:
x = 21/7
Simplifying the fraction, we find:
x = 3
Therefore, the length of the first piece is 2x = 2(3) = 6 feet, the length of the second piece is 5x = 5(3) = 15 feet, and the length of the third piece is 4 feet.
so what us the final answer?
The final answer is that the rope is cut into three pieces: the first piece is 6 feet long, the second piece is 15 feet long, and the third piece is 4 feet long.
the average of your 3 quiz grades is 17 points. two of your quiz grades are 14 points and 19 points. write and solve an equation to find the thrid quiz grade.
Let's assume the third quiz grade is represented by the variable "x".
According to the problem, the average of the three quiz grades is 17 points.
To find the average, we sum up all the grades and divide by the number of grades. In this case, we have:
(14 + 19 + x) / 3 = 17
Combining like terms, we get:
(33 + x) / 3 = 17
Next, we can multiply both sides of the equation by 3 to eliminate the fraction:
33 + x = 51
Finally, subtracting 33 from both sides of the equation, we can solve for x:
x = 51 - 33
Simplifying, we find:
x = 18
Therefore, the third quiz grade is 18 points.
you has $26 in your pocket. you purchaced x pens at $3.50 each. you now have $8.50 in your pocket. write and salve an equation to find the number pens purchased.
Let's assume that you purchased "x" pens.
Each pen costs $3.50, so the total cost of the pens can be represented as 3.50x.
You started with $26 in your pocket and after purchasing the pens, you had $8.50 left.
So, we can write the equation:
26 - 3.50x = 8.50
To solve for x, we need to isolate the variable on one side.
First, subtract 26 from both sides:
26 - 26 - 3.5x = 8.5 - 26
Simplifying,
-3.5x = -17.5
Next, divide both sides by -3.5 to solve for x:
(-3.5x) / -3.5 = (-17.5) / -3.5
Simplifying,
x = 5
Therefore, you purchased 5 pens.