Percent problems

Google Classroom

Problem

Cody was $165\,\text{cm}$165, start text, c, m, end text tall on the first day of school this year, which was $10\%$10, percent taller than he was on the first day of school last year.

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

 $\text{cm}$start text, c, m, end text

Hint #11 / 6

Cody's height on the first day of school this year was $10\%$10, percent taller than his height on the first day of school last year. He still had all $(100\%)$left parenthesis, 100, percent, right parenthesis of last year's height plus $10\%$10, percent more.

This year, he was $100\%+10\%=110\%$100, percent, plus, 10, percent, equals, 110, percent of his height from last year.

Hint #22 / 6

Percent means per hundred, so $\blueD{110\%}$start color #11accd, 110, percent, end color #11accd is equivalent to $\blueD{\dfrac{110}{100}}$start color #11accd, start fraction, 110, divided by, 100, end fraction, end color #11accd which is also equal to $\blueD{110\div 100}$start color #11accd, 110, divided by, 100, end color #11accd.

$\blueD{110\div 100 = 1.1}$start color #11accd, 110, divided by, 100, equals, 1, point, 1, end color #11accd

Hint #33 / 6

To find Cody's previous height, we need to answer, $\greenD{165\,\text{cm}}$start color #1fab54, 165, start text, c, m, end text, end color #1fab54 is $\blueD{110\%}$start color #11accd, 110, percent, end color #11accd of what height?

Hint #44 / 6

We can rewrite that question as an equation.

$\begin{array}{ccccc} \greenD{165\,\text{cm}}&\text{is}&\blueD{110\%}&\text{of}&\text{what height}\\\\ \greenD{165}&=&\blueD{1.1}&\times&? \end{array}$

Hint #55 / 6

Let's solve for the unknown height.

$\begin{aligned} \dfrac{\greenD{165}}{1.1}&=\dfrac{\blueD{1.1}\times?}{1.1}\\\\ 150&=? \end{aligned}$

Hint #66 / 6

Cody was $150\,\text{cm}$150, start text, c, m, end text tall on the first day of school last year.