Sure, let's solve this problem step-by-step.
We are given the statement "Thrice ' [tex]$p$[/tex] ' divided by 7 is equal to 35".
### Step 1: Translate the problem into an equation
"Thrice ' [tex]$p$[/tex] '" means 3 times the value of [tex]$p$[/tex]. So, we can write this as:
[tex]\[ 3p \][/tex]
"divided by 7" means we will divide this expression by 7, giving us:
[tex]\[ \frac{3p}{7} \][/tex]
According to the problem, this equals 35. So, we set up the equation:
[tex]\[ \frac{3p}{7} = 35 \][/tex]
### Step 2: Isolate [tex]$p$[/tex]
To solve for [tex]$p$[/tex], we need to isolate [tex]$p$[/tex] on one side of the equation. First, we'll clear the fraction by multiplying both sides of the equation by 7:
[tex]\[ 3p = 35 \times 7 \][/tex]
### Step 3: Simplify the right side
Next, we'll simplify the right side of the equation:
[tex]\[ 35 \times 7 = 245 \][/tex]
So, we have:
[tex]\[ 3p = 245 \][/tex]
### Step 4: Solve for [tex]$p$[/tex]
Now, we'll solve for [tex]$p$[/tex] by dividing both sides of the equation by 3:
[tex]\[ p = \frac{245}{3} \][/tex]
### Step 5: Simplify the result
Finally, let's simplify the division:
[tex]\[ p = 81.66666666666667 \][/tex]
Thus, the value of [tex]$p$[/tex] is:
[tex]\[ p = 81.66666666666667 \][/tex]
