# Simple algebra question

You drive $600$ miles in $2$ days. You drive $120$ miles less than you did on day one than on day $2$. How many miles did you drive both days separately? Solve algebraically.

$$d_1+d_2=600$$
$$d_2=d_1-120$$
Where do I go from here?

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Try replacing your second equation for d2 into the first one... – J. M. Apr 17 '11 at 3:42
Okay, so d1+d1-120=600? – user9681 Apr 17 '11 at 3:44
So then, d1+d1=480. d1=240. But 240-120= 120, and 120+240 is not equal to 600. – user9681 Apr 17 '11 at 3:48
$d_1 + d_1 - 120 = 600$ is correct, but you must add $120$ to each side, giving you $d_1 + d_1 = 720$, which should give you the right answer. – Alex Becker Apr 17 '11 at 4:13
Neal, the problem is that you made a mistake, you should get $720$ instead of $480$ because you're adding $600 + 120$ not subtracting. – Adrián Barquero Apr 17 '11 at 4:15

In these types of situations, you want to write one variable explicitly in terms of the other plus any other constants sticking around.

In this case you have :
equation 1 $$d_1+d_2=600$$ and equation 2
$$d_2=d_1-120$$ So you can replace $d_2$ in equation 1 by $d_1-120$, giving you:
$$d_1+(d_1-120)=600$$
$$2d_1 = 720$$
$$d_1 = 360$$

Then plug in $360$ into the second equation to solve for $d_2$, namely:
$$d_2 = 360 - 120 = 240$$

Edit: It seems you understand how it works well. You just made an algebraic mistake. The hard part is usually coming up with the equation, which you don't seem to have any trouble with! :) Edit2: As stated in the comments, the algebraic mistake is that you are subtracting from both sides $120$ rather than adding $120$.

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Thanks so much! – user9681 Apr 17 '11 at 5:02
You're very welcome! – fdart17 Apr 17 '11 at 15:57