How would you do this problem?

At the beginning of the year, the price of gasoline is $1.05 per gallon. The price increased $0.05 per gallon each week for the next 5 weeks. The price then decreased $0.07 per gallon for the next 3 weeks. Find the difference between the cost of 10 gallons at the beginning of the year and 10 gallons 8 weeks later. Show your work.

Cost of 10 gallons at beginning of year = 10 gallons x (1.05/gallon) = W

Price per gallon at end of 8 weeks is
1.05 + (5*0.05)+ (3*-.07) = Y
Cost of 10 gallons at end of 8 weeks is 10*Y.

Calculate the difference between Y and W.

$0.05 * 5 = $0.25

$1.05 + $0.25 = $1.30

$0.07 * 3 = $0.21

$1.30 - $0.21 = $1.09

10 * $1.05 = $10.50
10 * $1.09 = $10.90

$10.90 - 10.50 = ??

Thank you. I got $4.60, is that right?

Now I got $0.40, is that right now?

Yes. $0.40 is correct.

To solve this problem, we need to calculate the cost of 10 gallons of gasoline at the beginning of the year and 8 weeks later.

Let's break down the problem step by step:

Step 1: Calculate the cost of 10 gallons of gasoline at the beginning of the year.
At the beginning of the year, the price of gasoline is $1.05 per gallon. So, to find the cost of 10 gallons, we multiply the price per gallon by the number of gallons:

Cost at the beginning of the year = $1.05/gallon * 10 gallons

Step 2: Calculate the cost of 10 gallons of gasoline after 8 weeks.
The price increased $0.05 per gallon each week for the next 5 weeks, and then decreased $0.07 per gallon for the next 3 weeks.

To find the new price after 5 weeks, we need to add the weekly increase to the initial price for 5 weeks:
New price after 5 weeks = $1.05/gallon + ($0.05/gallon * 5 weeks)

To find the new price after 8 weeks, we need to subtract the decrease in price for the next 3 weeks:
New price after 8 weeks = New price after 5 weeks - ($0.07/gallon * 3 weeks)

Now, we can calculate the cost of 10 gallons of gasoline after 8 weeks:
Cost after 8 weeks = New price after 8 weeks * 10 gallons

Step 3: Calculate the difference in cost between the two scenarios.
To find the difference in cost between the cost at the beginning of the year and after 8 weeks, we subtract the cost at the beginning of the year from the cost after 8 weeks:

Difference in cost = Cost after 8 weeks - Cost at the beginning of the year

Now, let's substitute the values and calculate the result.