Difference between revisions of "2024 AMC 10A Problems/Problem 12"

Latest revision as of 19:40, 17 November 2024

Problem

Zelda played the Adventures of Math game on August 1 and scored $1700$ points. She continued to play daily over the next $5$ days. The bar chart below shows the daily change in her score compared to the day before. (For example, Zelda's score on August 2 was $1700 + 80 = 1780$ points.) What was Zelda's average score in points over the $6$ days?

$\textbf{(A)} 1700\qquad\textbf{(B)} 1702\qquad\textbf{(C)} 1703\qquad\textbf{(D)}1713\qquad\textbf{(E)} 1715$

Solution 1

Going through the table, we see her scores over the six days were: $1700$ , $1700+80=1780$ , $1780-90=1690$ , $1690-10=1680$ , $1680+60=1740$ , and $1740-40=1700$ .

Taking the average, we get $\frac{(1700+1780+1690+1680+1740+1700)}{6} = \boxed{\textbf{(E) } 1715}.$

-i_am_suk_at_math_2

Solution 2

Compared to the first day $(1700)$ , her scores change by $+80$ , $-10$ , $-20$ , $+40$ , and $+0$ . So, the average is $1700 + \frac{80-10-20+40+0}{6} = \boxed{\textbf{(E) }1715}$ .

-mathfun2012

Solution 3

As the scores of each day are dependent on previous days, we get: $1700 + \dfrac{0\cdot6 + 80\cdot5 + (-90)\cdot4 + (-10)\cdot3 + 60\cdot2 + (-40)\cdot1}{6} = \boxed{\textbf{(E) }1715}$

~NSAoPS

Video Solution by Pi Academy

https://youtu.be/ABkKz0gS1MU?si=ZQBgDMRaJmMPSSMM

Video Solution 1 by Power Solve

https://youtu.be/mfTDSXH9j2g

Video Solution by Daily Dose of Math

https://youtu.be/t8Dpj7dHZ3s

~Thesmartgreekmathdude

Video Solution by SpreadTheMathLove

https://www.youtube.com/watch?v=6SQ74nt3ynw

Video Solution by Just Math⚡

https://www.youtube.com/watch?v=o1Kiz_lZc90

@@ Line 1: / Line 1: @@
-Zelda played the ''Adventures of Math'' game on August 1 and scored <math>1700</math> points. She continued to play daily over the next <math>5</math> days. The bar chart below shows the daily change in her score compared to the day before. (For example, Zelda's score on August 2 was <math>1700 + 80 = 1780</math> points.) What was Zelda's average score in points over the <math>6</math> days?[[File:Example.jpg]]
+==Problem==
+Zelda played the ''Adventures of Math'' game on August 1 and scored <math>1700</math> points. She continued to play daily over the next <math>5</math> days. The bar chart below shows the daily change in her score compared to the day before. (For example, Zelda's score on August 2 was <math>1700 + 80 = 1780</math> points.) What was Zelda's average score in points over the <math>6</math> days?[[File:Screenshot_2024-11-08_1.51.51_PM.png]]
+<math>\textbf{(A)} 1700\qquad\textbf{(B)} 1702\qquad\textbf{(C)} 1703\qquad\textbf{(D)}1713\qquad\textbf{(E)} 1715</math>
+==Solution 1==
+Going through the table, we see her scores over the six days were: <math>1700</math>, <math>1700+80=1780</math>, <math>1780-90=1690</math>, <math>1690-10=1680</math>, <math>1680+60=1740</math>, and <math>1740-40=1700</math>.
+Taking the average, we get  <math>\frac{(1700+1780+1690+1680+1740+1700)}{6} = \boxed{\textbf{(E) } 1715}.</math>
+-i_am_suk_at_math_2
+==Solution 2==
+Compared to the first day <math>(1700)</math>, her scores change by <math>+80</math>, <math>-10</math>, <math>-20</math>, <math>+40</math>, and <math>+0</math>. So, the average is <math>1700 + \frac{80-10-20+40+0}{6} = \boxed{\textbf{(E) }1715}</math>.
+-mathfun2012
+==Solution 3==
+As the scores of each day are dependent on previous days, we get: <math>1700 + \dfrac{0\cdot6 + 80\cdot5 + (-90)\cdot4 + (-10)\cdot3 + 60\cdot2 + (-40)\cdot1}{6} = \boxed{\textbf{(E) }1715}</math>
+~NSAoPS
+== Video Solution by Pi Academy ==
+https://youtu.be/ABkKz0gS1MU?si=ZQBgDMRaJmMPSSMM
+==Video Solution 1 by Power Solve ==
+https://youtu.be/mfTDSXH9j2g
+== Video Solution by Daily Dose of Math ==
+https://youtu.be/t8Dpj7dHZ3s
+~Thesmartgreekmathdude
+==Video Solution by SpreadTheMathLove==
+https://www.youtube.com/watch?v=6SQ74nt3ynw
+==Video Solution by Just Math⚡==
+https://www.youtube.com/watch?v=o1Kiz_lZc90
+==See Also==
+{{AMC10 box|year=2024|ab=A|num-b=11|num-a=13}}
+{{MAA Notice}}

2024 AMC 10A (Problems • Answer Key • Resources)
Preceded by Problem 11	Followed by Problem 13
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