In July the price of a gallon of gas at Quick Fuel Gas Station rose 12%. In August it fell 15% of its final July price, ending the month at $2.29. What was the price at the beginning of July?

original price ---- x

(1.12)(.85)x = 2.29
x = ......

$X/gal. at beginning of July.

$1.12X/gal. after July increase.

Aug: 0.85 * $1.12X/gal. = $0.952X/gal..
0.952X = 2.29,
X = $2.41/gal.

Let's start by finding the price at the end of July.

If the price of gas at the Quick Fuel Gas Station rose 12% in July, we can calculate the price at the end of July by adding 12% to the initial price in July.

Let P be the initial price in July.

Price at the end of July = P + 12% of P

Price at the end of July = P + (12/100) * P

Price at the end of July = P + 0.12P

Price at the end of July = 1.12P

In August, the price fell 15% of its final July price. So, we can calculate the price at the end of August by subtracting 15% of the price at the end of July from the price at the end of July.

Price at the end of August = Price at the end of July - 15% of Price at the end of July

Price at the end of August = 1.12P - (15/100) * 1.12P

Price at the end of August = 1.12P - 0.168P

Price at the end of August = 0.952P

We are given that the price at the end of August is $2.29. So we can set up an equation to solve for P:

0.952P = $2.29

Dividing both sides by 0.952:

P = $2.29 / 0.952

P ≈ $2.40

Therefore, the price at the beginning of July was approximately $2.40.

To solve this problem, we can follow these steps:

Step 1: Let's assume the price at the beginning of July as "x".

Step 2: Calculate the 12% increase in July:
- Increase = (12/100) * x
- Final July price = x + Increase

Step 3: Calculate the 15% decrease in August:
- Decrease = (15/100) * Final July price
- Price at the end of August = Final July price - Decrease

Step 4: Set the final price in August equal to $2.29 and solve for x:
- Price at the end of August = $2.29
- Final July price - Decrease = $2.29

Let's solve the equations to find the price at the beginning of July:

x + (12/100) * x - (15/100) * (x + (12/100) * x) = $2.29

Step 5: Simplify the equation and solve for x:

x + 0.12x - 0.15(x + 0.12x) = $2.29

x + 0.12x - 0.15x - 0.018x = $2.29

0.952x = $2.29

x = $2.29 / 0.952

x ≈ $2.40

Therefore, the price at the beginning of July was approximately $2.40.