An "everyday math" problem that I need help in understanding

Question

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.

Answer 1

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.

Answer 2

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

Answer 3

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}