Question

In 2016, a group of p friends attended a movie together, and the tickets cost d dollars per person. By 2019, the cost of movie tickets had increased by 10% and the size of the group had increased by 5%. Find the percent increase in the total cost of the group attending a movie from 2016 to 2019.

Answer 1

15.5%

Explanation:

You want the percentage increase when p friends are charged d dollars each, after p increases by 5% and d increases by 10%.

Multiplier

If x increases by the fraction k, then the new total is ...

x + kx = x(1 +k)

When the increase is 10% = 0.10, the multiplier is (1 +0.10) = 1.10.

When the increase is 5% = 0.05, the multiplier is (1 +0.05) = 1.05.

Total effect

The new cost of the group attending a movie is ...

p(1.05) × d(1.10) = 1.155pd = (1 +0.155)pd

The increase in the product is 0.155 = 15.5%.

The increase in the total cost is 15.5%.

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Additional comment

This amounts to 10% +5% +(10%)(5%) = 15.5%.