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Cody was 
165cm tall on the first day of school this year, which was 
10% taller than he was on the first day of school last year.
How tall was Cody on the first day of school last year?
cm

Cody was 165 cm 165 \mathrm{~cm} tall on the first day of school this year, which was 10% 10 \% taller than he was on the first day of school last year.\newlineHow tall was Cody on the first day of school last year?\newlinecm \mathrm{cm}

Full solution

Q. Cody was 165 cm 165 \mathrm{~cm} tall on the first day of school this year, which was 10% 10 \% taller than he was on the first day of school last year.\newlineHow tall was Cody on the first day of school last year?\newlinecm \mathrm{cm}
  1. Understand Relationship: Understand the relationship between Cody's current height and his height last year.\newlineCody is currently 165cm165\,\text{cm} tall, which is 10%10\% taller than his height last year. This means that his height last year was the base height, and 165cm165\,\text{cm} is 110%110\% of that base height.
  2. Express Equation: Express the relationship in an equation.\newlineLet Cody's height last year be xx cm. Then, 110%110\% of xx is equal to 165165 cm. We can write this as:\newline110%110\% of x=165x = 165 cm
  3. Convert to Decimal: Convert the percentage to a decimal to use in the equation.\newline110%110\% as a decimal is 1.101.10. So the equation becomes:\newline1.10×x=1651.10 \times x = 165
  4. Solve for x: Solve for x by dividing both sides of the equation by 1.101.10. \newlinex=1651.10x = \frac{165}{1.10}\newlinex=150x = 150
  5. Verify Solution: Verify the solution.\newlineIf Cody was 150cm150\,\text{cm} tall last year, then a 10%10\% increase would be 150cm×0.10=15cm150\,\text{cm} \times 0.10 = 15\,\text{cm}. Adding this to his height last year gives us 150cm+15cm=165cm150\,\text{cm} + 15\,\text{cm} = 165\,\text{cm}, which matches the given current height.