If the present age of a grandfather is 80 years and the age of his grandson is 20 years, how many years ago was the grandfather 3 times as old as the grandson?
Practice Questions
1 question
Q1
If the present age of a grandfather is 80 years and the age of his grandson is 20 years, how many years ago was the grandfather 3 times as old as the grandson?
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Let x years ago, grandfather's age was 80 - x and grandson's age was 20 - x. We need 80 - x = 3(20 - x). Solving gives x = 10.
Questions & Step-by-step Solutions
1 item
Q
Q: If the present age of a grandfather is 80 years and the age of his grandson is 20 years, how many years ago was the grandfather 3 times as old as the grandson?
Solution: Let x years ago, grandfather's age was 80 - x and grandson's age was 20 - x. We need 80 - x = 3(20 - x). Solving gives x = 10.
Steps: 10
Step 1: Identify the current ages of the grandfather and grandson. The grandfather is 80 years old and the grandson is 20 years old.
Step 2: Define 'x' as the number of years ago we want to find out.
Step 3: Write the grandfather's age 'x' years ago. It will be 80 - x.
Step 4: Write the grandson's age 'x' years ago. It will be 20 - x.
Step 5: Set up the equation based on the condition that the grandfather was 3 times as old as the grandson 'x' years ago. The equation is 80 - x = 3(20 - x).
Step 6: Expand the equation: 80 - x = 60 - 3x.
Step 7: Rearrange the equation to isolate 'x'. Add 3x to both sides: 80 - x + 3x = 60. This simplifies to 80 + 2x = 60.
Step 8: Subtract 80 from both sides: 2x = 60 - 80, which simplifies to 2x = -20.
Step 9: Divide both sides by 2 to solve for 'x': x = -20 / 2, which gives x = -10.
Step 10: Since we are looking for how many years ago, we take the positive value of x, which is 10.
