Rational number word problems

Google Classroom

Problem

Ellis's backyard has a $6.25\,\text{m}$6, point, 25, start text, m, end text by $6.25\,\text{m}$6, point, 25, start text, m, end text patio. She would like to build a $1.5\,\text{m}$1, point, 5, start text, m, end text wide extension around $3$3 sides of the patio, as the figure shows. She will buy $0.25\,\text{m}$0, point, 25, start text, m, end text by $0.25\,\text{m}$0, point, 25, start text, m, end text tiles that come $25$25 to a package.

extension patio

How many packages does Ellis need to buy to build the extension?

 packages

Hint #11 / 5

Let's break up the extension into rectangles so we can determine its area.

$1.5\,\text{m}$$6.25\,\text{m}$$1.5\,\text{m}$

There are $3$3 rectangles that are $6.25\,\text{m}$6, point, 25, start text, m, end text by $1.5\,\text{m}$1, point, 5, start text, m, end text and $2$2 squares with a side length of $1.5\,\text{m}$1, point, 5, start text, m, end text.

$3\cdot6.25 \cdot 1.5 + 2 \cdot 1.5^2=32.625$3, dot, 6, point, 25, dot, 1, point, 5, plus, 2, dot, 1, point, 5, squared, equals, 32, point, 625

To build the extension, Ellis needs $32.625\,\text{m}^2$32, point, 625, start text, m, end text, squared of tile.

Hint #22 / 5

Each tile is $0.25\,\text{m}$0, point, 25, start text, m, end text wide and $0.25\,\text{m}$0, point, 25, start text, m, end text long. So Ellis needs $16$16 tiles to build $1\,\text{m}^2$1, start text, m, end text, squared of the extension.

$0.25\,\text{m}$$1\,\text{m}$

Hint #33 / 5

We can multiply the total area by the number of tiles to cover a square meter to find the total number of tiles Ellis needs.

$32.625\,\cancel{\text{m}^2} \cdot 16\,\dfrac{\text{tiles}}{\cancel{\text{m}^2}}=522\,\text{tiles}$32, point, 625, start cancel, start text, m, end text, squared, end cancel, dot, 16, start fraction, start text, t, i, l, e, s, end text, divided by, start cancel, start text, m, end text, squared, end cancel, end fraction, equals, 522, start text, t, i, l, e, s, end text

Hint #44 / 5

Ellis buys the tiles in packages of $25$25 tiles per package.

$\dfrac{522}{25}=20.88$start fraction, 522, divided by, 25, end fraction, equals, 20, point, 88

Since Ellis cannot buy part of a package, she will need $21$21 packages to have enough tiles.

Hint #55 / 5

Ellis needs to buy $21$21 packages of tiles to build the extension.