Understand simple problem on inflation If the average food basket costs $100$ euros at 2nd quarter prices, how much will it cost for 3rd quarter prices? Below is the graph. I know that the answer is $97$ and can be achieved using follows: $$100 \left( 1 - \left(\frac{97.5-95}{95}\right)\right)$$
But can someone explain me the logic behind this?

 A: The first computation is 
$$\left(\frac{97.5-95}{95}\right);$$
this is computing the ratio of the difference between second quarter price and third quarter price, on the third quarter price. That is, you are measuring the change in price between the second and third quarters relative to the third quarter price. If you multiply this ratio by $100$,
$$100\left(\frac{97.5-95}{95}\right),$$ you will get the amount by which this second quarter price (which is $100$) has dropped in the third quarter. You then substract this amount from $100$, the second quarter price:
$$100-100\left(\frac{97.5-95}{95}\right)=100\left(1-\left(\frac{97.5-95}{95}\right)\right).$$
A: A correct and simple way to solve this problem is:
$$ \require{cancel}100 \cancel{\text{ Q2 euros}} \cdot \frac{95 {\text{  Q3 euros}}}{97.5 \cancel{\text{ Q2 euros}}} = 97.44 \text{ Q3 euros} $$
We need to change units from units of Q2 euros to units of Q3 euros. This is like any change of units (eg. from feet to inches). For food, 95 euros in the 3rd quarter is equivalent to 97.5 euros in the 2nd quarter. Multiplying by the conversion factor $\frac{95 {\text{  Q3 euros}}}{97.5 \text{ Q2 euros}}$ is like multiplying by 1. For example:
$$ \require{cancel}2 \cancel{\text{ feet}} \cdot \frac{12 {\text{ inches}}}{1 \cancel{\text{ feet}}} = 24 \text{ inches} $$
This is an easy, less error prone way to change units.
Difference with the accepted answer
The accepted answer isn't quite precise. It says the percent increase from Q2 to Q3 is 1 minus the percent increase from Q3 to Q2:
$$ \frac{X_3 - X_2}{X_2} \approx 1 - \frac{X_2 - X_3}{X_3}$$
That's not a bad approximation for $X_2 \approx X_3$ but it's not quite right.
