Bryce spent x hours working on homework. He also spent 2x hours playing video games, and 1/2x hours watching television. If he spent 140 hours each week
doing these three things, how much time did he spend just on homework The length of a rectangle is 5 less than twice its width. The perimeter is 26
meters. Find the dimensions of the rectangle.

x=40 hours

Step-by-step explanation:

1/2x=watching television

x=time spent on homework

2x=time playing video games

The total amount of time spent doing all of these is 140 hours.

First: add up all the components and set them equal to the total time.

1/2x+x+2x=140

next solve for x by adding the variables and then dividing both sides by the number multiplied by x

3.5x=140

x=40

this gives you the value of x. Since the amount of time spent on homework is x, then the answer is 40 hours.

The perimeter of a rectangle is 2L+2W. Since we know that the perimeter is 26, then the equation to set up is 2L+2W=26, but it doesn't stop there. We are also told that the length is 5 less than the twice the width. To find this you set up a separate equation.

L=2W-5. You then substitute this equation in for L in the first equation

2(2W-5)+2W=26

From here you do the order of operations: PEMDAS

Parentheses: 2W-5- nothing can be simplified here

Exponents: There are no exponents

Multiplication: 2(2W-5)=4W-10      2W

Addition: 4W-10+2W=26 -> 6W-10=26

Subtraction: Though there is a number that is subtracted, it cannot be simplified on that side of the equal sign.

From here, we want to get W on its own on one side of the equal and everything that does not have W in it moved to the other side.

6W-10+10=26+10

6W=36

From here we want to isolate W from all numbers, so we divided both sides by 6

W=6

We now know the width, but wait! we now need to plug this back into the equation that gives us the length.

L=2W-5

L=2(6)-5

L=12-5

L=7

So, the length is 7 and the width is 5.