John and Jane went out for a dinner and they ordered the same dish. Both used a 10% discount coupon. John paid a 15% tip over the original price of the dish, while Jane paid the tip over the discounted price for the coupon. If John paid $0.63 more than Jane, what was the original price of the dish?
A. 24
B. 34.8
C. 37.8
D. 42
E. 84
The OA is D.
Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I'm not sure about how to solve it. I need your help. Thanks.
Hi swerve,
Let's take a look at your question.
Assume that the original price of the dish is x, then, the 10% discount on the dish can be calculated as:
$$Discount=\left(10\%\right)\times x$$
$$Discount=\left(\frac{10}{100}\right)\times x=0.1x$$
$$Discounted\ price\ of\ the\ dish=x-0.1x=0.9x$$
John paid a 15% tip over the original price of the dish i.e. x.
$$Tip\ John\ paid=\left(15\%\right)\left(x\right)=\left(\frac{15}{100}\right)x=0.15x$$
$$Amount\ John\ paid\ for\ the\ dinner=0.9x+0.15x=1.05x$$
Jane paid the tip over the discounted price for the coupon i.e. 0.9x
$$Tip\ Jane\ paid=\left(15\%\right)\left(0.9x\right)=\left(0.15\right)\left(0.9x\right)=0.135x$$
$$Amount\ Jane\ paid\ for\ the\ dinner=0.9x+0.135x=1.035x$$
The question states that John paid $0.63 more than Jane, it can be represented as:
$$Amount\ John\ paid\ =\ Amount\ Jane\ paid+0.63$$
$$1.05x=\ 1.035x+0.63$$
$$1.05x-1.035x=\ 0.63$$
$$0.015x=\ 0.63$$
$$x=\ \frac{0.63}{0.015}=42$$
Therefore, Option
D is correct.
Hope it helps.
I am available if you'd like any follow up.
