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

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Grade 7

Percent of change: find the original amount word problems

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Q. Cody was

165 \mathrm{~cm}

tall on the first day of school this year, which was

10 \%

taller than he was on the first day of school last year.

\newline

How tall was Cody on the first day of school last year?

\newline

______

\mathrm{cm}

Understand the problem: Understand the problem and what is being asked. $\newline$ Cody was $165\,\text{cm}$ tall on the first day of school this year, and this height is $10\%$ taller than his height on the first day of school last year. We need to find out Cody's height from last year.
Set up the equation: Set up the equation to find Cody's height from last year. $\newline$ Let Cody's height from last year be $x$ cm. According to the problem, Cody's height this year ( $165$ cm) is $10\%$ taller than last year. This means that Cody's height this year is $110\%$ of last year's height. So, we can write the equation as: $\newline$ $110\%$ of $x = 165$ cm
Convert to decimal: Convert the percentage to a decimal to use it in the equation. $\newline$ $110\%$ as a decimal is $1.10$ . So the equation becomes: $\newline$ $1.10 \times x = 165$
Solve for x: Solve for x to find Cody's height from last year. $\newline$ Divide both sides of the equation by $1.10$ to isolate $x$ : $\newline$ $x = \frac{165}{1.10}$
Perform division: Perform the division to calculate $x$ . $x = 150$
Verify solution: Verify the solution. $\newline$ If Cody was $150\,\text{cm}$ tall last year, then a $10\%$ increase would be $150\,\text{cm} \times 0.10 = 15\,\text{cm}$ . Adding this increase to last year's height should give us this year's height: $\newline$ $150\,\text{cm} + 15\,\text{cm} = 165\,\text{cm}$ $\newline$ Since this matches the given height for this year, our solution is correct.