Difference between revisions of "2023 AMC 12B Problems/Problem 4"

Revision as of 05:42, 16 November 2023

The following problem is from both the 2023 AMC 10B #4 and 2023 AMC 12B #4, so both problems redirect to this page.

Problem

Jackson's paintbrush makes a narrow strip with a width of 6.5 millimeters. Jackson has enough paint to make a strip 25 meters long. How many square centimeters of paper could Jackson cover with paint?

$\textbf{(A) } 162,500 \qquad\textbf{(B) } 162.5 \qquad\textbf{(C) }1,625 \qquad\textbf{(D) }1,625,000 \qquad\textbf{(E) } 16,250$

Solution 1

6.5 millimeters is equal to 0.65 centimeters. 25 meters is 2500 centimeters. The answer is $0.65 \times 2500$ , so the answer is $\boxed{\textbf{(C) 1,625}}$ .

~Failure.net ~Mintylemon66

Solution 2 (Standard Form)

6.5 millimeters can be represented as $65 \times 10^{-2}$ centimeters. 25 meters is $25 \times 10^{2}$ centimeters. Multiplying out these results in $(65 \times 10^{-2}) \times (25 \times 10^{2})$ , which is $65 \times 25$ making the answer $\boxed{\textbf{(C) 1,625}}$ .

~darrenn.cp

Video Solution 1 by SpreadTheMathLove

https://www.youtube.com/watch?v=SUnhwbA5_So

2023 AMC 10B (Problems • Answer Key • Resources)
Preceded by Problem 3	Followed by Problem 5
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 AMC 10 Problems and Solutions

2023 AMC 12B (Problems • Answer Key • Resources)
Preceded by Problem 3	Followed by Problem 5
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 AMC 12 Problems and Solutions

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

@@ Line 12: / Line 12: @@
 ~Mintylemon66
-==Solution 2(Standard Form)==
+==Solution 2 (Standard Form)==
-.5 millimeters can be represented as 65 \times 10^{-2} centimeters. 25 meters is 25 \times 10^{2} centimeters. Multiplying out these results in (65 \times 10^{-2}) \times (25 \times 10^{2}) which is 65 \times 25 , so the answer is <math>\boxed{\textbf{(C) 1,625}}</math>.
+.5 millimeters can be represented as <math>65 \times 10^{-2}</math> centimeters. 25 meters is <math>25 \times 10^{2}</math> centimeters. Multiplying out these results in <math>(65 \times 10^{-2}) \times (25 \times 10^{2})</math>, which is <math>65 \times 25</math> making the answer <math>\boxed{\textbf{(C) 1,625}}</math>.
 ~darrenn.cp

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