Ken and Paul each ordered a sandwich at a restaurant. The price of Ken's sandwich was $x$ dollars, and the price of Paul's sandwich was $$ 1$ more than the price of Ken's sandwich. If Ken and Paul split the cost of the sandwiches evenly and each paid a $20 %$ tip, which of the following expressions represents the amount, in dollars, each of them paid? (Assume there is no sales tax.)

0.2 x + 0.2

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0.5 x + 0.1

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1.2 x + 0.6

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2.4 x + 1.2

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Solution

The correct option is C $1.2 x + 0.6$
Since the price of Ken’s sandwich was $x$ dollars and Paul’s sandwich was $$ 1$ more, the price of Paul’s sandwich was $(x + 1)$ dollars.
Thus, the total cost of the sandwiches was $(2 x + 1)$ dollars.
Since this cost was split evenly, Ken and Paul each paid:
$\frac{2 x + 1}{2} = x + 0.5$
The fraction whose numerator is $(2 x + 1)$ and whose denominator is $2$ , equals $x + 0.5$ dollars plus a $20 %$ tip. After adding the $20 %$ tip, each of them paid:
$(x + 0.5) + 0.2 (x + 0.5) = 1.2 (x + 0.5) = 1.2 x + 0.6$ dollars.

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