Question

the differences between the years of birth and death of famous Egyptian women mathematican hypatia is 40 years old. two times the years of her birth exceed the year of her death by 335 years. find the year of her birth​

Answer 1

Answer:

Hypatia should have been born in the year 415.

Step-by-step explanation:

1. We know she lived for 40 years, so we can say that her birth year is some year $x$, and her death year is some year $x+40$.

2. The second part of the question says that $2x$, or two times her year of birth, is 335 more than her year of death, or $x+40$.

3. From 2, we can say that $2x=(x+40)+335$, and then solve for her birth year, x.

4. 2x=x+40+335

2x=x+375

x=375

5. If we plug this in, we can see that if she was born in the year 375. If we double this, we get the year 750. If we subtract 335 from this, because the problem says it should exceed her death year by that amount, we should get the year 415. Sure enough, $750-335=315$. If we simply add 40 to 375, we get the same answer: she would have lived until the year 415.

Answer 2

Answer:

Hypatia should have been born in the year 415.

Step-by-step explanation:

1. We know she lived for 40 years, so we can say that her birth year is some year xx , and her death year is some year x+40x+40 .

2. The second part of the question says that 2x2x , or two times her year of birth, is 335 more than her year of death, or x+40x+40 .

3. From 2, we can say that 2x=(x+40)+3352x=(x+40)+335 , and then solve for her birth year, x.

4. 2x=x+40+335

2x=x+375

x=375

5. If we plug this in, we can see that if she was born in the year 375. If we double this, we get the year 750. If we subtract 335 from this, because the problem says it should exceed her death year by that amount, we should get the year 415. Sure enough, 750-335=315750−335=315 . If we simply add 40 to 375, we get the same answer: she would have lived until the year 415.