Question

Найдите два двузначных числа, если известно, что сумма остальных двузначных чисел в 50 раз больше одного из этих двух чисел. В ответ запишите сумму этих чисел.

Answer 1

Сумма всех 90 двузначных чисел равна (10+99)*90/2=109*45=4905
Сумма двух чисел может быть от 10+11=21 до 98+99=197
Чтобы сумма оставшихся чисел делилась на 50, сумма двух вычеркнутых может быть равна 55,105, или 155.
1) Пусть сумма равна 55, тогда сумма оставшихся 4850, а одно число равно 4850/50=97. Не получается.
2) Пусть сумма равна 105, тогда сумма оставшихся 4800, а число 4800/50=96. А второе число 105-96=9. Не получается.
3) Пусть сумма чисел 155, тогда сумма оставшихся 4750. Одно число 4750/50=95, а второе 155-95=60.
Ответ: 95 и 60

Answer 2

Problem Analysis

We are given that the sum of all two-digit numbers is 50 times larger than one of the two-digit numbers. We need to find two two-digit numbers and calculate their sum.

Solution

Let's assume the two two-digit numbers are represented by a and b. According to the given information, the sum of all other two-digit numbers is 50 times larger than either a or b.

To find the sum of all two-digit numbers, we can use the formula for the sum of an arithmetic series: S = (n/2)(a + l), where S is the sum, n is the number of terms, a is the first term, and l is the last term.

In this case, the first term is 10 and the last term is 99. So, the sum of all two-digit numbers is S = (90/2)(10 + 99) = 45(109) = 4905.

Since the sum of all two-digit numbers is 50 times larger than either a or b, we can set up the following equation: 4905 = 50(a + b).

Simplifying the equation, we get: a + b = 4905/50 = 98.1.

Since we are looking for two two-digit numbers, we need to find two numbers whose sum is approximately 98.1. The closest two-digit numbers that add up to 98 are 49 and 49. Therefore, the sum of these two numbers is 49 + 49 = 98.

Answer

The sum of the two two-digit numbers is 98.

Explanation

We can find two two-digit numbers whose sum is 98 by solving the equation a + b = 98. The closest two-digit numbers that satisfy this equation are 49 and 49, which add up to 98.