Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 2.4 Junior Find the answer

Xiao Ming, a lover of ancient poetry, adapted the poem "Thoughts on a Still Night" by Su Shi after studying the chapter on quadratic equations: "The great river flows eastward, washing away all the heroes of the past. Standing at the age of thirty, overseeing Dongwu, he died young at a two-digit age. The tens digit is three less than the units digit, and the units digit squared equals his lifespan. Which student can calculate quickly, how many years did Zhou Yu live?" If the tens digit of Zhou Yu's age at death is $x$ , the equation can be written as:

Pick one

Solution

To solve the problem, let's break down the information given and translate it into a mathematical equation step by step:

1. Zhou Yu died at a two-digit age, where the tens digit is $x$ .
2. The tens digit is three less than the units digit. If the tens digit is $x$ , then the units digit is $x + 3$ .
3. The units digit squared equals his lifespan. This means $(x + 3)^2$ is equal to his age.

Now, let's construct the equation for his age using these pieces of information:

- The tens digit contributes $10x$ to his age.
- The units digit contributes $x + 3$ to his age.
- Therefore, his age can be represented as the sum of these two contributions: $10x + (x + 3)$ .

Given that the units digit squared equals his lifespan, we can equate this sum to the square of the units digit:

$10x + (x + 3) = (x + 3)^2$

This equation matches with option C: $10x + (x + 3) = (x + 3)^2$ .

Therefore, the correct equation that represents Zhou Yu's age, based on the given conditions, is:

$\boxed{C: 10x + (x + 3) = (x + 3)^2}$

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