Two-Stage Discount Calculation: What Will Daniel Pay for Pants?

To solve this problem, we'll sequentially apply the discounts.

• Step 1: Calculate the store discount (20% off).

• Step 2: Apply the membership discount (additional 10% off) on the reduced price.

Let's calculate:

Step 1: The store discount is 20%, so the price after the store discount is:

$\text{Price after 20\% discount} = \$150 \times (1 - 0.20)$

$\text{Price after 20\% discount} = \$150 \times 0.80 = \$120$

Step 2: With the membership card, Daniel gets an extra 10% discount on the already reduced price of $\$120$.

$\text{Price after additional 10\% discount} = \$120 \times (1 - 0.10)$

$\text{Price after additional 10\% discount} = \$120 \times 0.90 = \$108$

Therefore, the total amount Daniel needs to pay is $\$108$.

Hence, the correct choice is $2$: $108 \, \$$.