Question

Петя за месяц получил на пять пятерок больше, чем Маша, а Настя — на две пятерки меньше, чем Петя. Вместе Маша, Петя и Настя получили за месяц 98 пятерок. Сколько пятерок получила Настя?

Answer 1

Пусть Маша получила х пятерок, тогда Петя - х+5 пятерок, а Настя - х+5-2=х+3 пятерок.

Вместе они получили 98 пятерок

х+х+3+х+5=98
3х+8=98
3х=90
х=30
Значит Маша получила 30 пятерок, в Настя - 30+3=33 пятерки

Ответ: 33 пятерки

Answer 2

Let's use algebra to solve this problem step by step.

Let's represent the number of fives that Masha, Petya, and Nastya received as follows:

Let x be the number of fives that Masha received. Then, Petya received x + 5 fives (5 fives more than Masha). And Nastya received (x + 5) - 2 fives (2 fives less than Petya).

Now, the total number of fives they received is 98:

x + (x + 5) + ((x + 5) - 2) = 98.

Now let's solve for x:

x + x + 5 + x + 5 - 2 = 98 3x + 8 = 98 3x = 98 - 8 3x = 90 x = 90 / 3 x = 30.

Now that we know Masha received 30 fives, we can find how many fives Nastya got:

Nastya = (x + 5) - 2 = (30 + 5) - 2 = 35 - 2 = 33.

So, Nastya received 33 fives.