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I understand that you are supposed to use reverse percentages or maybe apply the Total amount payable formula, but I just don't know how. I've been at it for two hours now and I can't seem to figure it out. Can you please help me out here?

Here it is:

Khairul orders one set meal at a restaurant which offers a 20% discount. There is a service charge of 10% and GST is at 7%. Given that he pays a total of 23.54, find the marked price of the set meal.

I need a step by step solution. Preferably which explains what's going on in each step because I'm dumb.

max_zorn
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MirzaTheCutiePie
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3 Answers3

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Let x = meal price.

Then, $x*0.80*1.10*1.07 = 23.54$, and solving for x gives the meal price. To do this, divide both sides by $0.80*1.10*1.07$.

We multiply the meal price by 0.80 because that gives the price of a meal with a 20% discount. Multiplying by 1.10 adds the 10% tax, and multiplying by 1.07 adds the 7% tax.

Final Answer:

x = 23.54/(0.80*1.10*1.07) = 25

Further Clarification Let's imagine a simpler problem, where you pay for a meal with a 7% tax and the total, with tax, comes to 19.26\$.

Let x be the original meal cost.

Then, $x + x*0.07 = 19.26$ is an equation we can solve to determine the original meal cost. You take the cost of the meal, then add 7% of the meals cost to add the tax on. If we simplify the left hand side, we get $1x + 0.07x = 1.07x$. So, we need to solve $1.07x = 19.26$. Dividing both sides by 1.07 gives $x=18$.

Notice how the $1.07x$ appears as a result of collecting like terms, the original meal cost gives the 1 and the tax adds the 0.07.

JockoCigarNab
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  • Why do we add one to 10% and 7% to get 1.1 and 1.07? – MirzaTheCutiePie Sep 07 '18 at 21:43
  • Suppose you want to buy a 10 $ shirt with a 7% tax on it. Then, 10(1.07) = 10(1 + 0.07) = 10 + 0.70. Essentially, multiplying by 1.07 adds the tax onto the original cost. Another method would be to take 10 $ and add 10*0.07, similar to how rviertel does in his solution. – JockoCigarNab Sep 07 '18 at 21:57
  • I still don't understand. Can you try to explain it in a different way, because I'm stupid – MirzaTheCutiePie Sep 07 '18 at 22:00
  • You are not stupid, you are learning :) if we took x0.800.10*0.07, that would give us the cost of the tax, but what we want is the cost of the meal plus tax. Adding the 1 makes sure that the final answer includes the total cost. – JockoCigarNab Sep 07 '18 at 22:02
  • Yeah so I still don't understand. I get that it adds the cost of the meal but why? Why does it add the cost of the meal? (Apologies if I'm sounding like a child here) – MirzaTheCutiePie Sep 07 '18 at 22:05
  • I made an edit to my answer, please let me know if that helped. – JockoCigarNab Sep 07 '18 at 22:37
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    Oooh so it's like proportions so 100% will be 18 and 107% will be 19.26 – MirzaTheCutiePie Sep 08 '18 at 07:25
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Let x be the price of the meal.

Assuming that the service charge is applied to the marked price and that tax is applied on top of the final amount charged by the restaurant, we would have

(x - .2x + .1x) * 1.07 = 23.54

.9x = 23.54/(1.07)

x = 23.54/(1.07)/(0.9) = 24.44
rviertel
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    Note the difference between my answer and JockoCigarNab's answer is whether the service charge and tax is applied before or after the discount – rviertel Sep 07 '18 at 21:43
  • I would think that typically tax is applied after a discount, but a service charge (i.e. a tip?) is normally applied to the marked price – rviertel Sep 07 '18 at 21:45
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    A restaurant I use frequently applies an automatic service charge on the pretax amount, with or without a prior discount. Ambiguous questions are a pain. – Phil H Sep 07 '18 at 21:49
  • Indeed the order in which these discounts or charges are applied matters a great deal. It is certainly open for debate unless there is a more precise (or less ambiguous) writing of the question at hand. – M A Pelto Sep 07 '18 at 21:57
  • This is the method that they used last time I went to Olive Garden so I'm sticking with my answer :-) – rviertel Sep 07 '18 at 22:01
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Let $x$ denote the marked price of the meal.

We have the following three equations to solve for $x$

$x - 0.2x = y$

$y+0.1y = z$

$z+0.07z=23.54$

Since $0.8x = y$ we may substitute $0.8x$ for $y$ into the equation $1.1y=z$ to get the equation $0.88x=z$. Now we may substitute $0.88x$ for $z$ into the equation $1.07z=23.54$ to get the equation $0.9416x=23.54$. Hence we have \begin{equation}x=\frac{23.54}{0.9416}=25. \end{equation}

M A Pelto
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