You are 78 years old. The phrase “400 reduced by 2 times my age is 244” translates into the equation 400 − 2x = 244, where x is your age. Solving that equation gives x = 78.
How to Set Up the Equation
The trick with word problems like this is converting everyday language into math. Each phrase maps to a specific operation:
- “Reduced by” means subtraction. “400 reduced by something” means 400 minus that something.
- “2 times my age” means multiplication: 2 × your age.
- “Is” means equals.
Put it all together and you get: 400 − 2x = 244, where x represents your age in years.
Solving Step by Step
Start with the equation:
400 − 2x = 244
Subtract 244 from both sides and add 2x to both sides to isolate the variable:
400 − 244 = 2x
156 = 2x
Divide both sides by 2:
x = 78
To double-check, plug 78 back in: 400 − (2 × 78) = 400 − 156 = 244. It checks out.
Why the Wording Trips People Up
“Reduced by 2 times” can feel ambiguous at first glance. You might wonder whether it means “divided by 2” or “subtract 2 times something.” In standard math language, “reduced by” consistently means subtraction. If the problem meant division, it would say “divided by” or “the quotient of.” Meanwhile, “2 times my age” is straightforward multiplication. The full phrase “reduced by 2 times my age” therefore means: subtract (2 × age) from the starting number.
A common mistake is computing 244 − 400 = −156 and then dividing by −2 correctly to still get 78. That works, but watch the signs. One tutor’s published solution accidentally wrote −145 instead of −156, which would give the wrong answer of 72.5. Small arithmetic errors like swapping digits are the biggest pitfall in problems this simple.
Applying This Pattern to Similar Problems
Age riddles almost always follow the same structure: take a starting number, apply one or two operations involving an unknown age, and set the result equal to a given value. If you see “increased by,” that means addition. “The product of” signals multiplication. “The quotient of” means division. Once you match each English phrase to its operation, you can write the equation and solve it the same way you did here, by isolating x on one side.