Answer:
At the end of the second week, the gas costs $2.79 per gallon.
Step-by-step explanation:
This can be solved by two rules of three, as they are percentage problems.
In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.
When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too. In this case, the rule of three is a cross multiplication.
When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease. In this case, the rule of three is a line multiplication.
Percentage problems are an example of rule of three with direct relationship between the measures.
How much does gas cost at the end of the second week?
The first step is seeing how much the gas cost at the end of the first week.
The problem states that at the start of the month the cost of gas was $3.09 per gallon. The price went up 12.9% after the first week. So, $3.09 is 100% = 1 decimal. The final is going to be 100%+12.9% = 112.9% = 1.129 of $3.09. So
3.09 - 1
x - 1.129
[tex]x = 3.09*1.129[/tex]
[tex]x = $3.49[/tex]
The cost at the end of the first week is $3.49.
The cost at the end of the second week:
The problem states that from the end of the first week to the end of the second week the price decreased by 20.1%. So, $3.49 is 100% = 1. The final cost is going to be 100%-20.1% = 79.9% = 0.799 of $3.49. So
3.49 - 1
x - 0.799
[tex]x = 3.49*0.799[/tex]
[tex]x = $2.79[/tex]
At the end of the second week, the gas costs $2.79 per gallon.
