The sum of four times a first number and a second number is 68. If the first number is decreased by twice the second number the result is -1. Find the numbers.

The first number is 15 and the second number is 8.

Step-by-step explanation:

Let us assume,

Given :

Sum of four times a first number and a second number is 68.

⇒ 4x + y = 68

⇒ y = 68-4x

If the first number is decreased by twice the second number the result is -1.

⇒ x - 2y = -1

Substitute y = 68-4x in the above equation.

⇒ x - 2(68-4x) = -1

⇒ x-136+8x = -1

⇒ 9x - 136 = -1

⇒ 9x = -1+136

⇒ x = 135/9

⇒ x = 15

The first number is 15.

The second number is y = 68-4x.

⇒ y = 68 - 4(15)

⇒ y = 68-60

⇒ y = 8

The second number is 8.

Step-by-step explanation:

You are now a teacher, and you notice that many of your students are consistently making the dividing-out mistake that appears below. Some of the students even admit to knowing the method was wrong as soon as you point it out.

Create a visual to help your students stop making this common mistake: fraction numerator up diagonal strike x squared plus 3 x − 4 over denominator up diagonal strike x squared − 2 x − 8 end fraction .

Your lesson should do the following:

Explain why the dividing-out method is incorrect. You may want to start with a simpler expression and work your way up to polynomials. (For example, compare fraction numerator 3 left parenthesis 5 right parenthesis over denominator 3 end fraction and fraction numerator 3 plus 5 over denominator 3 end fraction.)

Explain when you can cancel a number that is in both the numerator and denominator and when you cannot cancel out numbers that appear in both the numerator and the denominator.

Share tricks, reminders, memory devices, or other methods to help students catch themselves before making this common mistake.

Post your video or series of images. Post answers to the following questions:

A. Why do you think the mistake shown here is such a common one?

B. Have you ever made this mistake before? What helped you stop making this mistake? What will help you stop making this mistake in the future?

Read and comment on the explanations of other student “teachers.”

A. Comment on ideas that helped you better understand or tricks to help you catch yourself before making the dividing-out mistake.

B. Ask a question to help a student improve his or her explanation or make it more thorough.

Respond to replies to your post.

Be sure to check back regularly to participate in the discussion with your fellow students and teacher.

P.S. I can not see pictures or videos that are posted on here, so if you could write everything out it would be kindly appreciated. :)