Discussion

Find a single discount which is equivalent to three successive discounts of 15%, 16% & 20%.

Answer: C

Multiply the three retained fractions.

\[ (1-0.15)(1-0.16)(1-0.20) = 0.85 \times 0.84 \times 0.80 \]

\[ 0.85 \times 0.84 = 0.714, \qquad 0.714 \times 0.80 = 0.5712 \]

\[ \text{single equivalent discount} = 1 - 0.5712 = 0.4288 = 42.88\% \]

The rates sum to 51%, far above the truth. The order of the three discounts makes no difference, since multiplication is commutative.

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