If a cost total needs to be reduced by a 9% discount, what should that total be multiplied by?
A.
109/100
B.
9/10
C.
9/100
D.
91/100
D. 91/100
To calculate the total after a 9% discount, you need to multiply the total by the fraction representing the remaining amount after the discount has been applied.
The remaining amount after a 9% discount is 100% - 9% = 91%.
Therefore, the total should be multiplied by 91/100.
Therefore, the correct answer is D. 91/100.
To reduce a cost total by a 9% discount, you need to multiply it by a certain factor. Let's go through the steps to find this factor:
Step 1: Calculate the discount rate. To do this, divide the discount percentage (9%) by 100: 9/100 = 0.09.
Step 2: Calculate the discount factor. The discount factor represents the amount by which the cost total should be reduced. To find it, subtract the discount rate from 1: 1 - 0.09 = 0.91.
Step 3: Calculate the factor to multiply the cost total by to achieve the desired reduction. This factor is the reciprocal of the discount factor from step 2. In other words, it is the fraction 1 over the discount factor: 1 / 0.91 = 1.0989 (rounded to four decimal places).
Now, let's compare this factor to the answer choices:
A. 109/100: This is actually the reciprocal of 100/109, so it does not match the calculated factor.
B. 9/10: This is the reciprocal of 10/9, so it does not match the calculated factor.
C. 9/100: This is not even the reciprocal of the discount factor, so it does not match the calculated factor.
D. 91/100: Finally, this answer choice matches the calculated factor of 1.0989.
Therefore, the correct answer is option D. The total should be multiplied by 91/100 to achieve a 9% discount.