Track / Stage 5 / 270 of 400 #870 of 1964

Problem 870

AIME late

Algebra Difficulty 5.6 Find the answer

4. Mr. Perić arrived in Matkograd on Friday and ordered a taxi. The driver explained that the departure fee is 20 kuna, plus an additional 5 kuna for each kilometer traveled. On Saturday, he used the services of the same taxi company, but that day, due to the anniversary of the company's founding, all driving bills were reduced by $20 \%$ . That day, Mr. Perić traveled $5 \mathrm{~km}$ more than on Friday, and he paid the same amount of money. How many kilometers did Mr. Perić travel on Friday, and how many on Saturday, and how much did he pay for one taxi ride?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Official solution

4. Let $\mathrm{s} x$ be the number of kilometers Mr. Perić walked on Friday.

For this distance, he would have to pay $[20+5 x]$ kuna since there was no discount on Friday.

1 POINT

On Saturday, Mr. Perić walked $5 \mathrm{~km}$ more, i.e., $[x+5]$ kilometers, which would cost him $[20+(5(x+5))]$ kuna, or $[45+5 x]$ kuna,

but with a $20 \%$ discount, he pays $80 \%$ of the price, which means he pays [0.8 (45 + 5x)] kuna, or $[36+4 x]$ kuna.

1 POINT

Since he paid the same amount of money on Saturday as on Friday, the equation is

$0.8(45+5 x)=20+5 x$ ,

1 POINT

$36+4 x=20+5 x$ ,

$x=16$ . 1 POINT

Therefore, Mr. Perić walked $16 \mathrm{~km}$ on Friday and $21 \mathrm{~km}$ on Saturday. 1 POINT

For one ride, he paid $20+16 \cdot 5=20+80=100$ kuna. 1 POINT

TOTAL 6 POINTS

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.