Question 1209779: The sum of quarter of what Elijah's age was 4 yrs ago and double of what it will be in 2 yrs is 66.
How old is Eliyah?
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Let's solve this problem step-by-step.
**1. Define the Variable**
Let E be Elijah's current age.
**2. Translate the Word Problem into an Equation**
* "4 years ago": Elijah's age was E - 4
* "Quarter of what Elijah's age was 4 years ago": (1/4)(E - 4)
* "2 years from now": Elijah's age will be E + 2
* "Double of what it will be in 2 years": 2(E + 2)
* "The sum of quarter of what Elijah's age was 4 years ago and double of what it will be in 2 years is 66": (1/4)(E - 4) + 2(E + 2) = 66
**3. Solve the Equation**
* (1/4)(E - 4) + 2(E + 2) = 66
* (E - 4)/4 + 2E + 4 = 66
* Multiply the entire equation by 4 to eliminate the fraction:
* E - 4 + 8E + 16 = 264
* Combine like terms:
* 9E + 12 = 264
* Subtract 12 from both sides:
* 9E = 252
* Divide both sides by 9:
* E = 28
**4. Check the Answer**
* 4 years ago, Elijah was 28 - 4 = 24. A quarter of that is 24/4 = 6.
* In 2 years, Elijah will be 28 + 2 = 30. Double that is 30 * 2 = 60.
* 6 + 60 = 66. The answer checks.
**Therefore, Elijah is 28 years old.**
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