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

Simple patterns, variables, the order of operations, simplification, evaluation, linear equations and graphs, etc.
1492wasblue
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Joined: Tue Jul 28, 2009 5:34 pm

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

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

is there a formula for this?

stapel_eliz
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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?

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

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.

1492wasblue
Posts: 4
Joined: Tue Jul 28, 2009 5:34 pm

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

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

jordierocks94
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### Re: two numbers. The difference is 24 and the sum is 60.

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.

stapel_eliz
Posts: 1628
Joined: Mon Dec 08, 2008 4:22 pm
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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.