Age Application Part 2

[mathdad]

Ten years from now, Cory will be three times older than he is today. Set up the equation(s) that lead to his current age. DO NOT solve.

Solution:

Let C = Cory's age today

C + 10 = 3C

Note: There is nothing more important to me in the world of math than mastering the art of creating an equation(s) from word problems. If I can somehow "master" this art, this skill, I would be completely satisfied as far as math is concerned.

 

[tkhunny]

Ten years from now, Cory will be three times older than he is today. Set up the equation(s) that lead to his current age. DO NOT solve.

Solution:

Let C = Cory's age today

C + 10 = 3C

Note: There is nothing more important to me in the world of math than mastering the art of creating an equation(s) from word problems. If I can somehow "master" this art, this skill, I would be completely satisfied as far as math is concerned.

You have already learned the MOST important thing. WRITE DOWN clear, accurate, and sufficient definitions.

 

[Steven G]

Now solve it! Just because the questions says to not solve doesn't mean that you should not solve iy!!

 

[mathdad]

You have already learned the MOST important thing. WRITE DOWN clear, accurate, and sufficient definitions.

I struggle with the art of creating equations from word problems. This is an easy question.

 

[mathdad]

Now solve it! Just because the questions says to not solve doesn't mean that you should not solve iy!!

C + 10 = 3C

C - 3C = -10

-2C = -10

C = -10/-2

C = 10/2

C = 5

Cory is 5 years old.

 

[Steven G]

C + 10 = 3C

C - 3C = -10

-2C = -10

C = -10/-2

C = 10/2

C = 5

Cory is 5 years old.

In C + 10 = 3C if you erased the 10 what would you replace it with to get a valid equation. Answer-- C + 2C = 3C. So 2C=10 and C =5

One more point to make. Since you are solving for C bring the C's to the side that has more C's. This way you will never get negative C's
So C + 10 =3C
10 = 3C-C
10=2C
C=5
Or use the short cut I showed above

 

[mathdad]

In C + 10 = 3C if you erased the 10 what would you replace it with to get a valid equation. Answer-- C + 2C = 3C. So 2C=10 and C =5

One more point to make. Since you are solving for C bring the C's to the side that has more C's. This way you will never get negative C's
So C + 10 =3C
10 = 3C-C
10=2C
C=5
Or use the short cut I showed above

Good notes for my math files.

 

[tkhunny]

Good notes for my math files.

Now, we're getting the idea.

 

[mathdad]

More age word problems in a few days.

 

[Harry_the_cat]

C + 10 = 3C

C - 3C = -10

-2C = -10

C = -10/-2

C = 10/2

C = 5

Cory is 5 years old.

Yes 5 years old is correct. Did you take your solution all the way back to the word problem (not your equation) and check that it is correct.

In other words, if Cory is 5 years old, will he be 3 times as old as he is now in 10 years time? In this case yes!!

It's always a good idea to check your answer back in the original wordy question! If it doesn't make sense then

1. your equation was incorrect
or
2. Your equation was correct but you solved it incorrectly.

 

[mathdad]

Yes 5 years old is correct. Did you take your solution all the way back to the word problem (not your equation) and check that it is correct.

In other words, if Cory is 5 years old, will he be 3 times as old as he is now in 10 years time? In this case yes!!

It's always a good idea to check your answer back in the original wordy question! If it doesn't make sense then

1. your equation was incorrect
or
2. Your equation was correct but you solved it incorrectly.

I always check my work.

 

[tkhunny]

The real question is, HOW do you check your work. If your standard is 14/20, what happened to the other 6?

 

[mathdad]

The real question is, HOW do you check your work. If your standard is 14/20, what happened to the other 6?

The passing score is 14/20 correct answers. The six incorrect questions I post here. If I get less than 14/20, I repeat the section until it is completely understood.

 

[tkhunny]

Nonresponsive. If you check your work, how do you miss ANY? This is my question.

 

[mathdad]

Nonresponsive. If you check your work, how do you miss ANY? This is my question.

After completing a section, I select 20 questions found at the end of the section. I select odd number questions. After answering all 20 questions, I check the answers in the back of the book. This is how I know if 14/20 has been achieved.

 

[tkhunny]

After completing a section, I select 20 questions found at the end of the section. I select odd number questions. After answering all 20 questions, I check the answers in the back of the book. This is how I know if 14/20 has been achieved.

I see. So, in other words, you have no idea what "check your own work" actually means. I demonstrate.

Ten years from now, Cory will be three times older than he is today. How old is Cory, today?

C = Cory's Age Today
C+10 = Cory's Age in 10 Years
3*C = Cory's Age in 10 Years

Done Translating and Defining. Now the equation

C+10 = 3*C

Now Solving

10 = 3C - C = 2C
5 = C

Done Solving. Now we check our work. This requires that we use the earliest existence of any known relationships or equations.

Equation: C+10 = 3C
Proposed Result: C = 5

C + 10 = 5 + 10 = 15
3*C = 3*5 = 15

Excellent. Our solution appears to satisfy the constraints.

Done with Checking. Done with the problem. Move on to the next problem.

Note: "Look in the back of the book," was NOT part of this demonstration. Nor has this action much value at all in my opinion. It may be described more accurately as "Giving Yourself a Grade", rather than "Checking Your Answers".

 

[tkhunny]

Here's another possible version. I'll make a mistake in purpose.

Ten years from now, Cory will be three times older than he is today. How old is Cory, today?

C = Cory's Age Today
C+10 = Cory's Age in 10 Years
3*C = Cory's Age in 10 Years

Done Translating and Defining. Now the equation

C+10 = 3*C

Now Solving

C - 3C = 10 <== Did you see the error? Play like we didn't notice.
-2C = 10
C = 10/(-2) = -5 <== This is a silly result, but let's play like we failed to notice.

Done Solving. Now we check our work. This requires that we use the earliest existence of any known relationships or equations.

Equation: C+10 = 3C
Proposed Result: C = -5

C + 10 = -5 + 10 = 5
3*C = 3*(-5) = -15

Wait! 5 and -15 are not the same thing!! Something bad must have happened along the way. Let's go back and find it before we move on.

We do not need the back of the book to tell us that something went wrong. It's called "Checking Your Own Work".

 

[mathdad]

I see. So, in other words, you have no idea what "check your own work" actually means. I demonstrate.

Ten years from now, Cory will be three times older than he is today. How old is Cory, today?

C = Cory's Age Today
C+10 = Cory's Age in 10 Years
3*C = Cory's Age in 10 Years

Done Translating and Defining. Now the equation

C+10 = 3*C

Now Solving

10 = 3C - C = 2C
5 = C

Done Solving. Now we check our work. This requires that we use the earliest existence of any known relationships or equations.

Equation: C+10 = 3C
Proposed Result: C = 5

C + 10 = 5 + 10 = 15
3*C = 3*5 = 15

Excellent. Our solution appears to satisfy the constraints.

Done with Checking. Done with the problem. Move on to the next problem.

Note: "Look in the back of the book," was NOT part of this demonstration. Nor has this action much value at all in my opinion. It may be described more accurately as "Giving Yourself a Grade", rather than "Checking Your Answers".

I know what "check your own work" means. After finding the value of a variable, I plug it back into the original question to make sure that I get the same answer on both sides of the equation.

 

[mathdad]

Here's another possible version. I'll make a mistake in purpose.

Ten years from now, Cory will be three times older than he is today. How old is Cory, today?

C = Cory's Age Today
C+10 = Cory's Age in 10 Years
3*C = Cory's Age in 10 Years

Done Translating and Defining. Now the equation

C+10 = 3*C

Now Solving

C - 3C = 10 <== Did you see the error? Play like we didn't notice.
-2C = 10
C = 10/(-2) = -5 <== This is a silly result, but let's play like we failed to notice.

Done Solving. Now we check our work. This requires that we use the earliest existence of any known relationships or equations.

Equation: C+10 = 3C
Proposed Result: C = -5

C + 10 = -5 + 10 = 5
3*C = 3*(-5) = -15

Wait! 5 and -15 are not the same thing!! Something bad must have happened along the way. Let's go back and find it before we move on.

We do not need the back of the book to tell us that something went wrong. It's called "Checking Your Own Work".

I get it. No need to nail me to the cross. Take it easy. I am just having fun with math.

 

[tkhunny]

After completing a section, I select 20 questions found at the end of the section. I select odd number questions. After answering all 20 questions, I check the answers in the back of the book. This is how I know if 14/20 has been achieved.

No one is angry or nailing or even slightly excited. You said you looked in the back to check your work. If you meant something else, you should have said so. Anyway, why not practice with the even-numbered exercises? They're in the book for a reason.