Answer :
Certainly! Let's solve the problem step-by-step using the information provided.
### Step 1: Set Up the System of Equations
We want to find out how many weekdays [tex]\( x \)[/tex] and weekend days [tex]\( y \)[/tex] Jamal parked his car, given the following:
1. Jamal parked for a total of 6 days:
[tex]\[
x + y = 6
\][/tex]
2. The total cost for parking was [tex]$52. The weekday parking cost is $[/tex]7 per day, and the weekend parking cost is $12 per day. This gives us:
[tex]\[
7x + 12y = 52
\][/tex]
### Step 2: Solve for [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex]
From the first equation [tex]\( x + y = 6 \)[/tex], solve for [tex]\( y \)[/tex]:
[tex]\[
y = 6 - x
\][/tex]
### Step 3: Substitute [tex]\( y \)[/tex] in the Second Equation
Now substitute [tex]\( y = 6 - x \)[/tex] into the second equation [tex]\( 7x + 12y = 52 \)[/tex]:
[tex]\[
7x + 12(6 - x) = 52
\][/tex]
### Step 4: Simplify and Solve for [tex]\( x \)[/tex]
1. Distribute the 12:
[tex]\[
7x + 72 - 12x = 52
\][/tex]
2. Combine like terms:
[tex]\[
-5x + 72 = 52
\][/tex]
3. Subtract 72 from both sides:
[tex]\[
-5x = 52 - 72
\][/tex]
[tex]\[
-5x = -20
\][/tex]
4. Divide by -5 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{-20}{-5} = 4
\][/tex]
### Step 5: Find [tex]\( y \)[/tex]
Now that we have [tex]\( x = 4 \)[/tex], use the equation [tex]\( y = 6 - x \)[/tex] to find [tex]\( y \)[/tex]:
[tex]\[
y = 6 - 4 = 2
\][/tex]
### Conclusion
Jamal parked his car for 4 weekdays and 2 weekend days.
### Step 1: Set Up the System of Equations
We want to find out how many weekdays [tex]\( x \)[/tex] and weekend days [tex]\( y \)[/tex] Jamal parked his car, given the following:
1. Jamal parked for a total of 6 days:
[tex]\[
x + y = 6
\][/tex]
2. The total cost for parking was [tex]$52. The weekday parking cost is $[/tex]7 per day, and the weekend parking cost is $12 per day. This gives us:
[tex]\[
7x + 12y = 52
\][/tex]
### Step 2: Solve for [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex]
From the first equation [tex]\( x + y = 6 \)[/tex], solve for [tex]\( y \)[/tex]:
[tex]\[
y = 6 - x
\][/tex]
### Step 3: Substitute [tex]\( y \)[/tex] in the Second Equation
Now substitute [tex]\( y = 6 - x \)[/tex] into the second equation [tex]\( 7x + 12y = 52 \)[/tex]:
[tex]\[
7x + 12(6 - x) = 52
\][/tex]
### Step 4: Simplify and Solve for [tex]\( x \)[/tex]
1. Distribute the 12:
[tex]\[
7x + 72 - 12x = 52
\][/tex]
2. Combine like terms:
[tex]\[
-5x + 72 = 52
\][/tex]
3. Subtract 72 from both sides:
[tex]\[
-5x = 52 - 72
\][/tex]
[tex]\[
-5x = -20
\][/tex]
4. Divide by -5 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{-20}{-5} = 4
\][/tex]
### Step 5: Find [tex]\( y \)[/tex]
Now that we have [tex]\( x = 4 \)[/tex], use the equation [tex]\( y = 6 - x \)[/tex] to find [tex]\( y \)[/tex]:
[tex]\[
y = 6 - 4 = 2
\][/tex]
### Conclusion
Jamal parked his car for 4 weekdays and 2 weekend days.
