Question

решите пожалуйста решая олимпиадную задачу ученик допустил ошибку. При сложении двух целых чисел по ошибке поставил во втором слагаемом лишний нуль на конце и получил в сумме 6641 вместо 2411. Определите слагаемые

Answer 1

Пусть правильная пара чисел была a,b

Тогда неправильная 10a,b

Имеет место система:

$<span>\left \{ {{a+b=2411} \atop {10a+b=6641}} \right$

$10a+2411-a=6641$

$9a=4230$

$a=470$

$b=2411-a=2411-470=1941$

Answer 2

Problem Analysis

The student made a mistake by adding an extra zero at the end of the second term, resulting in a sum of 6641 instead of 2411. We need to determine the two addends.

Solution

Let's assume the two addends are x and y. According to the problem, the sum of x and y is 6641. However, the student mistakenly added an extra zero to the second term, so the second term is actually 10 times larger than it should be. This means the correct second term should be y/10.

We can set up the following equation to represent the problem: x + y/10 = 664