To solve for the demand [tex]\( d \)[/tex] when the price [tex]\( p(d) \)[/tex] is given by the function [tex]\( p(d) = 10 - \frac{d}{3} \)[/tex] and the price [tex]\( p \)[/tex] is 8, follow these steps:
1. Start with the given price equation:
[tex]\[ p(d) = 10 - \frac{d}{3} \][/tex]
2. Substitute the given price [tex]\( p = 8 \)[/tex] into the equation:
[tex]\[ 8 = 10 - \frac{d}{3} \][/tex]
3. To isolate [tex]\( d \)[/tex], first move the constant term on the right side to the left side of the equation by subtracting 10 from both sides:
[tex]\[ 8 - 10 = - \frac{d}{3} \][/tex]
4. Simplify the left side:
[tex]\[ -2 = - \frac{d}{3} \][/tex]
5. To eliminate the negative sign on the right side, multiply both sides by -1:
[tex]\[ 2 = \frac{d}{3} \][/tex]
6. Finally, solve for [tex]\( d \)[/tex] by multiplying both sides of the equation by 3:
[tex]\[ d = 2 \times 3 \][/tex]
[tex]\[ d = 6 \][/tex]
Therefore, the demand [tex]\( d \)[/tex] when the price is 8 is:
B. 6
