  # Quick question with QoD

<p>I understand the problem and I got it right the second time around. However I don't necessarily understand what I used before to get my first answer is wrong. It made sense to me. Please clarify. </p>

<p>I first tried:</p>

<p>y=2x/2 - z OR y= 2(1/2)x - z</p>

<p>I tried to solve for 2 half gallons. </p>

<p>I got: x-y-z=0 And needless to say, it was wrong. </p>

<p>So I saw the word equation then I thought maybe let's not solve for x....??? and let's see where that gets me.
And I tried:
y=2x-z
0=2x-y-z And it was correct.</p>

<p>So my question is why don't you just simplify x? It's two half gallons which makes it one gallon, right?</p>

<p>I just answered this in another math question thread if you want to see my explanation.</p>

<p>I'm a bit lost on what you were trying to do the first time around but I'll just write it out again.</p>

<p>X is the price of the half gallon and Y is the price of the full gallon (which is usually cheaper). They are asking for Z, which is the price difference between buying two 1/2 gallons of milk (2x) compared to buying one full gallon (y).</p>

<p>2x-y=z or 2x-y-z=0 to match the answer choices</p>

<p>If you did this in the grocery store to see whether or not it is benefitial to purchase two half gallons or one full gallon it would look like this:</p>

<p>Half Gallon: \$1.98
Gallon: \$3.89</p>

<p>2(1.98)-3.89= .07 -----> The difference is seven cents (which would be z in the question).</p>

<p>Ok I'll clarify. If there are 2 half gallons, why not simplify it and make it 1 gallon while trying to find the equation? So instead of 2(1/2)X=(2/2)X=X. If X=1/2 and we need two of X, why don't we just plug it in and it makes 1. Do you get that logic...or do I still need to clarify?</p>

<p>^ But X is defined as 1/2 of a gallon. That is, a half of a gallon is X, not 1/2 of X. The mistake you're making is that you're looking at X as "1/2 of a gallon" and then concluding that because it's only half of a gallon, it should be half of X. But because X is a half of a gallon, two half gallons is 2X, not X. </p>

<p>That was probably an awful explanation, but it made sense in my mind!</p>

<p>But Y is the full gallon, X is the half gallon. So 2x is equivalent to y in terms of volume.</p>

<p>The variable X represents a half gallon, X is not a full gallon that is written down as 1/2x.
So to set X equal to one full gallon you would double x, not double 1/2x. </p>

<p>I hope something clicks with that explanation.</p>

<p>
[quote]
^ But X is defined as 1/2 of a gallon. That is, a half of a gallon is X, not 1/2 of X. The mistake you're making is that you're looking at X as "1/2 of a gallon" and then concluding that because it's only half of a gallon, it should be half of X. But because X is a half of a gallon, two half gallons is 2X, not X. </p>

<p>That was probably an awful explanation, but it made sense in my mind!

[/quote]
</p>

<p>Somestudent2, you beat me to it.</p>

<p>2x=1 Gallon
y = 1 Gallon</p>

<p>2x - z = 1
2x - y - z = 0</p>

<p>I get it thanks guys! :) I was looking at X as it was half instead of it representing half. I understand X=1/2 so, 2x=1. Not x/2. Bc that would be saying I am halving X. The way I ws doing it before meant that I was taking half of the half gallon. Thanks again!</p>