Percent problems

Google Classroom

Problem

Haruka hiked several kilometers in the morning. She hiked only $6$6 kilometers in the afternoon, which was $25\%$25, percent less than she had hiked in the morning.

How many kilometers did Haruka hike in all?

 kilometers

Hint #11 / 6

Haruka walked $25\%$25, percent fewer kilometers in the afternoon, so she walked $100\%-25\%=\blueD{75\%}$100, percent, minus, 25, percent, equals, start color #11accd, 75, percent, end color #11accd as many kilometers in the afternoon as in the morning.

She walked $\greenD{6}$start color #1fab54, 6, end color #1fab54 kilometers $(\text{km})$left parenthesis, start text, k, m, end text, right parenthesis in the afternoon.

Hint #22 / 6

Percent means per hundred, so $\blueD{75\%}$start color #11accd, 75, percent, end color #11accd is equivalent to $\blueD{\dfrac{75}{100}}$start color #11accd, start fraction, 75, divided by, 100, end fraction, end color #11accd which is also equal to $\blueD{75\div 100}$start color #11accd, 75, divided by, 100, end color #11accd.

$\blueD{75\div 100 = 0.75}$start color #11accd, 75, divided by, 100, equals, 0, point, 75, end color #11accd

Hint #33 / 6

To find how far Haruka hiked in the morning, we need to answer, $\greenD{6\,\text{km}}$start color #1fab54, 6, start text, k, m, end text, end color #1fab54 is $\blueD{75\%}$start color #11accd, 75, percent, end color #11accd of what distance?

Hint #44 / 6

We can rewrite that question as an equation.

$\begin{array}{ccccc} \greenD{6\,\text{km}}&\text{is}&\blueD{75\%}&\text{of}&\purpleD{\text{what distance}}\\\\ \greenD{6}&=&\blueD{0.75}&\times&\purpleD{?} \end{array}$

Hint #55 / 6

Let's solve for the unknown distance.

$\begin{aligned} \dfrac{\greenD{6}}{0.75}&=\dfrac{\blueD{0.75}\times\purpleD{?}}{0.75}\\\\ \purpleD{8}&=\purpleD{?} \end{aligned}$

Haruka hiked $\purpleD{8\,\text{km}}$start color #7854ab, 8, start text, k, m, end text, end color #7854ab in the morning and $\greenD{6\,\text{km}}$start color #1fab54, 6, start text, k, m, end text, end color #1fab54 in the afternoon. How far did she hike in all?

Hint #66 / 6

Haruka hiked a total of $\purpleD{8\,\text{km}}+\greenD{6\,\text{km}}=14\,\text{km}$start color #7854ab, 8, start text, k, m, end text, end color #7854ab, plus, start color #1fab54, 6, start text, k, m, end text, end color #1fab54, equals, 14, start text, k, m, end text in all.