Let's analyze the given problem step-by-step to identify the correct equation and value of [tex]\( x \)[/tex], the distance of 1 lap around the path at the park:
We are given:
- Florian ran 1.2 miles.
- Florian walked 4.8 laps around the path.
- The total distance covered is 3.6 miles.
We need to find [tex]\( x \)[/tex], the distance of one lap around the path.
First, let’s write the equation representing the total distance:
[tex]\[ \text{Ran distance} + \text{Walked distance} = \text{Total distance} \][/tex]
Which can be expressed as:
[tex]\[ 1.2 + 4.8x = 3.6 \][/tex]
Next, let's isolate [tex]\( x \)[/tex]:
1. Subtract 1.2 from both sides of the equation:
[tex]\[ 4.8x = 3.6 - 1.2 \][/tex]
[tex]\[ 4.8x = 2.4 \][/tex]
2. Divide both sides by 4.8:
[tex]\[ x = \frac{2.4}{4.8} \][/tex]
[tex]\[ x = 0.5 \][/tex]
Thus, the correct equation and value for [tex]\( x \)[/tex] is [tex]\( 4.8x + 1.2 = 3.6 \)[/tex], and the value of [tex]\( x \)[/tex] is [tex]\( 0.5 \)[/tex] miles.
Reviewing the options given:
1. [tex]\( 6x + 12 = 4.8 \)[/tex]; [tex]\( x = 1 \)[/tex] mile (this option is not correct)
2. [tex]\( 4.8x + 1.2 = 3.6 \)[/tex]; [tex]\( x = 0.5 \)[/tex] mile (this option is correct)
3. [tex]\( 3.6x + 1.2 = 4.8 \)[/tex]; [tex]\( x = 1 \)[/tex] mile (this option is not correct)
4. [tex]\( 4.8x + 1 \cdot 2 = 3.6 \)[/tex]; [tex]\( x = 1 \)[/tex] mile (this option is not correct)
Therefore, the correct equation is [tex]\( 4.8x + 1.2 = 3.6 \)[/tex] with [tex]\( x = 0.5 \)[/tex] mile.
