SOLUTION: The difference of two numbers is 33. The second is 7 less than 3 times the first. What are the two numbers?

Question 80665: The difference of two numbers is 33. The second is 7 less than 3 times the first. What are the two numbers?
Found 4 solutions by praseenakos@yahoo.com, Shin123, MathTherapy, ikleyn:
Answer by praseenakos@yahoo.com(507)   (Show Source): You can put this solution on YOUR website!
QUESTION:

The difference of two numbers is 33. The second is 7 less than 3 times the first. What are the two numbers?

ANSWER:

Let us assume that one number is x.

Three times of x can be written as 3x.

7 less than 3 times the first can be written as 3x - 7.

Then we can take the other number as 3x - 7.

It is given that their difference is 33.

So we can write, first number -second number = 33

That is x - (3x-7) = 33

==> x - 3x + 7 = 33 ( remove the parenthesis by multiplying each term inside it with -1.)

==> -2x + 7 = 33. ( x - 3x = -2x)

Subtract 7 from both sides of the equation. Then we have,

-2x + 7 - 7 = 33 - 7

==> -2x = 26

Now divide both sides of the equation by -2.

==> -2x/-2 = 26/-2

==> x = -13.

So the first number is -13.

We have second number = 3x - 7

= 3(-13) - 7

= -39 - 7

= -46.

So the numbers are -13 and -46.

To check the answer....find the difference of these numbers.

That is -13 - (-46) = -13 + 46 = 33.That is our answer is correct.

Hope you understood.

Regards.

Praseena.

Answer by Shin123(626)   (Show Source): You can put this solution on YOUR website!
x=first y=second

in other words,

so

I don�t think I solved it correctly.
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

The difference of two numbers is 33. The second is 7 less than 3 times the first. What are the two numbers?

Correct answer:
Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.

x = first y = second x - y = 33 (1) according to the condition y = 3x-7 (2) according to the condition Substitute (2) into (1) to get x - (3x-7) = 33 x - 3x + 7 = 33 -2x = 33 - 7 -2x = 26 x = -13 ====> y = 3x-7 = 3*(-13) - 7 = -39-7 = -46. Answer. The numbers are -13 (first) and -46 (second).

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Notice:   The words "the difference of two numbers" may mean (x-y) OR (y-x) - it is not determined by an unique way.

So, playing with the difference y-x = 33, you will get another answer.

Try it and get your own answer/solution.

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