two numbers. The difference is 24 and the sum is 60.  TOPIC_SOLVED

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two numbers. The difference is 24 and the sum is 60.

Postby 1492wasblue on Sat Aug 01, 2009 1:19 am

There are two numbers. The difference is 24 and the sum is 60. What are the two numbers?

is there a formula for this?
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Postby stapel_eliz on Sat Aug 01, 2009 12:42 pm

There isn't a "formula", per se, such as one might use for finding the area of a triangle. But there is logic.

In your case, you have two numbers. They are twenty-four units apart. This means that one of them is twenty-four more than the other. When you add them, you are, in effect, adding some equal amount to itself, and then adding in another twenty-four.

If the total is sixty, what then (working backwards) must be that equal amount? Then what are the two numbers? :wink:

If you get stuck, please reply showing your work and reasoning so far. Thank you! :D
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Re: two numbers. The difference is 24 and the sum is 60.

Postby sdbielz on Sat Aug 01, 2009 2:02 pm

I agree with the last post, that's the way I would do it. I do, however, think it would behoov you in the long run to learn how to translate it into an algebraic equation.

there are three elements to this problem. (Something)+(something else)=60.

Lets call 'something' X. so now...

X+(something else)=60

Since we know that the difference between the added numbers is 24, we can call 'something else' (X-24). And now we have:

X+(X-24)=60

With some simplification, we have 2X-24=60.

Now just solve for X.
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Re: two numbers. The difference is 24 and the sum is 60.

Postby 1492wasblue on Wed Aug 05, 2009 10:38 pm

So 60 - 24 = 36, 36/2 = 18, 18 + 24 = 42

checking: 42 - 18 = 24 and 42 + 18 = 60

the numbers are 18 and 42

Thanks
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Re: two numbers. The difference is 24 and the sum is 60.

Postby jordierocks94 on Wed Aug 26, 2009 8:06 am

Question about clarification of the process -- When Adding the two equations [ ( x + y = 60 ) + ( x - y = 24 ) ] and result was 2x = 84. The reason nothing was done with the "y" variable at that point is because first 2x = 84 had to be Simplified, Solved and then plugged in value of x to equations to Solve for "y;" is that the correct approach, sequence and description.

Thanks.
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Postby stapel_eliz on Wed Aug 26, 2009 11:08 am

Actually, no. Something was "done with the y variable": -y and +y were added, resulting in zero.

This system was solved by addition / elimination, rather than substitution. This is an equally-valid solution method. Unless the instructions specify that one use substitution, it is not "the" correct method, but merely one of many. :wink:
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