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

Latest revision as of 21:53, 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

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

@@ Line 7: / Line 7: @@
 == Solution 1 ==
-We need <math>12/cdot9</math> square feet of carpet to cover the room's floor.  Since there are <math>9</math> square feet in a square yard, you divide this by <math>9</math> to get <math>12</math> square yards, so our answer is <math>\bold{\boxed{\textbf{(A) }12}}</math>.
+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>, 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>3\cdot4=\boxed{\textbf{(A) }12}</math>.
+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)==

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