Last year, the price of a vacation package was \(P.\) At the beginning of this year, the price went up 40%. Lucas used a

Vincen wrote: ↑

Tue Apr 28, 2020 8:12 am

Last year, the price of a vacation package was \(P.\) At the beginning of this year, the price went up 40%. Lucas used a travel voucher to purchase the vacation package at 30% off this year’s price. In terms of \(P,\) how much did Lucas pay?

(A) \(P + 10\)
(B) \(1.1\cdot P\)
(C) \(1.12\cdot P\)
(D) \(0.9\cdot P\)
(E) \(0.98\cdot P\)

[spoiler]OA=E[/spoiler]

Source: Magoosh

Given

Price of the package last year = P
Price of the package this year = P + 40% of P = P + 0.4*P = 1.4*P

Since Lucas got a 30% discount on this year's price, he has to pay 70% of the price of the package this year.

Price paid by Lucas to buy the package = 70% of (1.4*P) = 0.98*P

The correct answer: E

Hope this helps!

-Jay
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Vincen wrote: ↑

Tue Apr 28, 2020 8:12 am

Last year, the price of a vacation package was \(P.\) At the beginning of this year, the price went up 40%. Lucas used a travel voucher to purchase the vacation package at 30% off this year’s price. In terms of \(P,\) how much did Lucas pay?

(A) \(P + 10\)
(B) \(1.1\cdot P\)
(C) \(1.12\cdot P\)
(D) \(0.9\cdot P\)
(E) \(0.9\cdot P\)

[spoiler]OA=E[/spoiler]

Source: Magoosh

With the voucher, Lucas paid P x 1.4 x 0.7 = 0.98P this year.

(Note: there is a typo, and choice E should read 0.98P)

Answer: E