Difference between revisions of "2015 AMC 8 Problems/Problem 1"

Latest revision as of 22:53, 16 January 2025

Problem

Onkon wants to cover his room's floor with his favourite red carpet. How many square yards of red carpet are required to cover a rectangular floor that is $12$ feet long and $9$ feet wide? (There are 3 feet in a yard.)

$\textbf{(A) }12\qquad\textbf{(B) }36\qquad\textbf{(C) }108\qquad\textbf{(D) }324\qquad \textbf{(E) }972$

Solution 1

We need $12\cdot9$ square feet of carpet to cover the floor. Since there are $9$ square feet in a square yard, we divide this by $9$ to get $\bold{\boxed{\textbf{(A) }12}}$ square yards.

Solution 2

Since there are $3$ feet in a yard, we divide $9$ by $3$ to get $3$ yards, and $12$ by $3$ to get $4$ yards. To find the area of the carpet, we then multiply these two values together to get $3\cdot4=\boxed{\textbf{(A) }12}$ square yards.

Video Solution 1 (HOW TO THINK CRITICALLY)

https://youtu.be/8mpjdpKcFs8

~Education, the Study of Everything

Video Solution 2

https://youtu.be/758_W_eK81g

~savannahsolver

2015 AMC 8 (Problems • Answer Key • Resources)
Preceded by First Problem	Followed by Problem 2
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AJHSME/AMC 8 Problems and Solutions

These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions.

@@ Line 1: / Line 1: @@
-How many square yards of carpet are required to cover a rectangular floor that is <math>12</math> feet long and <math>9</math> feet wide? (There are 3 feet in a yard.)
+==Problem==
+Onkon wants to cover his room's floor with his favourite red carpet. How many square yards of red carpet are required to cover a rectangular floor that is <math>12</math> feet long and <math>9</math> feet wide? (There are 3 feet in a yard.)
 <math>\textbf{(A) }12\qquad\textbf{(B) }36\qquad\textbf{(C) }108\qquad\textbf{(D) }324\qquad \textbf{(E) }972</math>
-==Solution==
+== Solution 1 ==
+We need <math>12\cdot9</math> square feet of carpet to cover the floor.  Since there are <math>9</math> square feet in a square yard, we divide this by <math>9</math> to get <math>\bold{\boxed{\textbf{(A) }12}}</math> square yards.
+== Solution 2 ==
+Since there are <math>3</math> feet in a yard, we divide <math>9</math> by <math>3</math> to get <math>3</math> yards, and <math>12</math> by <math>3</math> to get <math>4</math> yards. To find the area of the carpet, we then multiply these two values together to get <math>3\cdot4=\boxed{\textbf{(A) }12}</math> square yards.
+==Video Solution 1 (HOW TO THINK CRITICALLY)==
+https://youtu.be/8mpjdpKcFs8
+~Education, the Study of Everything
+==Video Solution 2==
-First, we multiply <math>12\cdot9</math> to get that you need <math>108</math> square feet of carpet you need to cover.  Since there are <math>9</math> square feet in a square yard, you divide <math>108</math> by <math>9</math> to get <math>12</math> square yards, so our answer is <math>\boxed{\textbf{(A)}~12}</math>.
+https://youtu.be/758_W_eK81g
-==Solution 2==
+~savannahsolver
-Since there are <math>3</math> feet in a yard, we divide <math>9</math> by <math>3</math> to get <math>3</math>, and <math>12</math> by <math>3</math> to get <math>4</math>. To find the area of the carpet, we then multiply these two values together to get <math>\boxed{\textbf{(A)}~12}</math>
 ==See Also==
 {{AMC8 box|year=2015|before=First Problem|num-a=2}}
 {{MAA Notice}}
+[[Category:Introductory Geometry Problems]]

Page

Toolbox

Search