Answer:
The discount percentage is about 13.2%.
Explanation:
Representing the situation with an equation:
We know that the difference of the original amount and the discount (i.e., the discount percentage * the original amount) equals the new amount:
original amount - (discount percentage * original amount) = new amount
Thus, we can determine the percentage using the equation O - P%O = N, where
- O represents the original amount (i.e., $18.05),
- P represents the percentage as a decimal,
- and N represents the new amount (i.e., $15.67).
Solving for P and converting to a percentage
Now, we substitute 18.05 for O and 15.67 for N in our equation to solve for P, the percentage as a decimal.
(18.05 - 18.05P = 15.67) - 18.05
(-18.05P = -2.38) / -18.05
P = 0.1318559557
P = 0.132
Finally, we convert the decimal to a percentage by multiplying 0.132 by 100:
P = 0.132 * 100
P = 13.2
Thus, the discount percentage is 13.2%.
Optional: Check the validity of the answer:
We can check that our answer is correct by substituting 0.132 for P in the equation and seeing if we get 15.67 on both sides:
18.05 - 0.132 * 18.05 = 15.67
18.05 - 2.3826 = 15.67
15.6674 = 15.67
15.67 = 15.67
Thus, our answer is correct.