Sally's age is 7 years
Step-by-step explanation:
The given is:
- Sally squares the number representing her age
- The result is 14 more than 5 times her age
We need to find Sally's age
Assume that the number representing the Sally's age is x
∵ Sally squares the number representing her age
∵ The number representing the Sally's age is x
∵ The result is 14 more than 5 times her age
- Square x and equate it by 14 plus 5 times x
∴ x² = 14 + 5x
- Subtract 5x from both sides
∴ x² - 5x = 14
- Subtract both sides by 14
∴ x² - 5x - 14 = 0
Now lets solve the quadratic equation to find the value of x
Factorize the left hand side into two factors
∵ x² = x × x
∵ 14 = 2 × 7
∴ 2x - 7x = -5x
∴ (x - 7) and (x + 2) are the factors of x² - 5x - 14
∴ (x - 7)(x + 2) = 0
- Equate each factor by 0
∵ x - 7 = 0
- Add both sides by 7
∴ x = 7
∵ x + 2 = 0
- Subtract 2 from both sides
∴ x = -2 ⇒ rejected no age represents by negative number
∴ The number representing Sally's age is 7
To check the answer
Square 7 and add 14 to 5 times 7, both must give you the same answers
∵ 7² = 49
∵ 14 + 5 × 7 = 14 + 35 = 49
Both gave the same answers, then the answer is right
Sally's age is 7 years
Learn more:
You can learn more about the word problems in brainly.com/question/13101704
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