Question

Ephraim took a friend for a birthday dinner. The total bill for dinner was $30.29 (including tax and a tip). If Ephraim paid a 22.3% tip, what was his bill before adding the tip?
(Round your answer to the nearest cent.)

Answer 1

Answer:

$x= 30.29 (1-0.223) = 23.54$

Ephraim paid a 22.3% tip, what was his bill before adding the tip?

23.54

Step-by-step explanation:

For this case we assume the following notation:

$T= 30.29$ represent the total paid for the dinner

x represent the amount before adding the tip

f =0.223 represent the fraction of the total amount destined to the tip

Based on this we can create the following relationship between T and x:

$T = f*T + (1-f)T = f*T + x$

And we can solve for x from the previous equation like this:

$x = T - f*T$

Taking T common factor we got:

$x = T (1-f)$

And if we replace we got:

$x= 30.29 (1-0.223) = 23.54$

And the amount destined to the tip would be $fT = 0.223*30.29=6.75$

And if we add the two values we see that:

23.54+6.75 = 30.29 representing the total cost.

So then the correct answer for the question:

Ephraim paid a 22.3% tip, what was his bill before adding the tip?

23.54