Question

При сложении двух натуральных чисел Ваня ошибочно поставил лишний нуль в конце одного из слагаемых и получил в сумме 4857 вместо 1617. Какие числа он складывал?

Answer 1

$\left \{ {{x+y=1617} \atop {10x+y=4857}} \right. \\ \\ \left \{ {{x=1617-y} \atop {10(1617-y)+y=4857}} \right. \\ \\ 16170-9y=4857\\ y=1257\\ x=360$

Answer 2

Solution:

To solve this problem, we can use a system of equations to find the two natural numbers that Vanya was adding.

Let's denote the two natural numbers as A and B. According to the given information, Vanya mistakenly added an extra zero to one of the numbers. This means that the correct sum of A and B is 1617, but Vanya obtained 4857 due to the error.

We can express this information in the following equations:

1. A + B = 1617 2. 10A + B = 4857

Now, let's solve this system of equations to find the values of A and B.

First, we can subtract the first equation from the second equation to eliminate B:

10A + B - (A + B) = 4857 - 1617 9A = 3240 A = 360

Now that we have the value of A, we can substitute it back into the first equation to solve for B:

360 + B = 1617 B = 1617 - 360 B = 1257

Answer:

So, the two natural numbers that Vanya was adding are 360 and 1257.