Question 1120734
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The distance traveled (and therefore presumably the amount of petrol used) is multiplied by a factor of (1-x/100); the price is multiplied by a factor of (1+y/100).  The total cost of the petrol is<br>
(1-x/100)(1+y/100) = 1+y/100-x/100-xy/10000<br>
The change in the cost of the petrol is<br>
y/100-x/100-xy/10000<br>
Multiplying by 100 to get the change as a percentage, the percent change in the cost is y-x-xy/100.<br>
Note we don't know whether that is an increase or a decrease in total cost.<br>
Example 1:
Decrease travel by 10% when the price increases by 20% (x=10,y=20)
The distance traveled gets multiplied by (1-.10) = .90; the price gets multiplied by (1+.20) = 1.20
The total cost gets multiplied by (.90)(1.20) = 1.08, an increase of 8%
By the formula, 20-10-200/100 = 10-2 = 8 percent<br>
Example 2:
Decrease travel by 30% when the cost increases by 10% (x=30, y=10)
The distance traveled gets multiplied by (1-.30) = .70; the price gets multiplied by (1+.10) = 1.10
The total cost gets multiplied by (.70)(1.10) = 0.77, an decrease of 23%
By the formula, 10-30-300/100 = -20-3 = -23 percent<br>