MORE ALGEBRA HELP! 2 questions?

Question

1) Solve this system of equations: y=x-10

5y+10=10

2)The difference of two numbers is 10. Two times the larger number is 20 more than the smaller. What are the 2 numbers?

THANK YOU

Answer 1

Folllow this solution of a question llike number 2.  If you can follow this, you can do number 2.

The difference of two numbers is 16.  Three times the smaller number is 12 more than the larger.  What are the two numbers?

Step 1:  Understand the question.  (Sometimes, replacing "number" with "age" or "dollars" makes it easier to follow.)

Step 2:  Ask "What is the question asking for?"  Here, it is asking for TWO numbers.

Step 3:  WRITE DOWN a letter for each of the unknown values like this:

...............  Let x denote the larger number.

...............  Let y denote the smaller number.

Make it a habit to always WRITE THIS DOWN.  You will benefit as the years go by.

Step 4:  Because you have TWO unknown values, you need to read the question and discover TWO equations.  (Three unknown values, three equations ...)

Step 5:  Take the first sentence and write a corresponding equation.    

Since x is larger than y, we have  x - y = 16.

Now, take the second sentence and write a corresponding equation.

"Three times the smaller number" would mean 3y.

"Twelve more than the larger (number)" would mean 12 + x.

The word "is" in between says they are equal.

This gives us 3y = 12 + x.

Now, we have TWO equations.

Step 6:  Solve the set of equations (using substitution or elimination).

Since x - y = 16, x = y + 16

Substituting y + 16 in for x in the second equation gives us:

3y = 12 + (y + 16)  or  3y = y + 28

This gives us 2y = 28 and y = 14.

Since y = 14, x = 14 + 16 = 30

Step 7:  WRITE OUT "The two numbers are 14 and 30."

Step 8:  Check your solution.  (Checking is quick.  ALWAYS check.)

"Is the difference between 14 and 30 equal to 16?"  Sure.

"Is three times the 14 the same as 12 more than 30?"  Both are 42.  Sure.

Note: Use only Step 6 above to do 1).

Remember:  Mathematics will be useful in life by dealing with word problems like "Should we move or how much insurance should we carry or how much chicken should I purchase today expecting all of these people to come to dinner tomorrow?"  Get good on word problems and life will be better.