Question

type the correct answer in each box. use numerals instead of words. micah is keeping track of how much he spends this month on gas. in the first week, he bought x gallons of gas at $2.39 per gallon. in the second week, he bought 3 fewer gallons of gas than the first week at $2.49 per gallon. so far this month, he has spent a total $45.21 on gas. in the first week, micah bought \square gallons of gas. in the second week, micah bought \square gallons of gas.

Explanation:

Step1: Define variables and set up equation

Let \( x \) be the number of gallons bought in the first week. Then the number of gallons bought in the second week is \( x - 3 \). The cost for the first week is \( 2.39x \) dollars, and the cost for the second week is \( 2.49(x - 3) \) dollars. The total cost is \( 46.21 \) dollars, so we set up the equation:
\[ 2.39x + 2.49(x - 3) = 46.21 \]

Step2: Expand and simplify the equation

First, expand \( 2.49(x - 3) \):
\[ 2.39x + 2.49x - 7.47 = 46.21 \]
Then combine like terms (\( 2.39x + 2.49x \)):
\[ 4.88x - 7.47 = 46.21 \]

Step3: Solve for \( x \)

Add \( 7.47 \) to both sides of the equation:
\[ 4.88x = 46.21 + 7.47 \]
\[ 4.88x = 53.68 \]
Then divide both sides by \( 4.88 \):
\[ x = \frac{53.68}{4.88} \]
\[ x = 11 \]

Step4: Find the number of gallons in the second week

The number of gallons in the second week is \( x - 3 \), so substitute \( x = 11 \):
\[ 11 - 3 = 8 \]

Answer:

In the first week, Micah bought \( \boldsymbol{11} \) gallons of gas.
In the second week, Micah bought \( \boldsymbol{8} \) gallons of gas.