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Difference between revisions of "2024 AMC 10A Problems/Problem 12"
 
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As the strongest curse Jogoat, fought the fraud, the king of curses, he began to open his domain. Sukuna shrunk back in fear, then Jogoat said, "Stand proud Sukuna. You are strong."
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==Problem==
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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]]
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<math>\textbf{(A)} 1700\qquad\textbf{(B)} 1702\qquad\textbf{(C)} 1703\qquad\textbf{(D)}1713\qquad\textbf{(E)} 1715</math>
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 +
==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>.
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 +
Taking the average, we get  <math>\frac{(1700+1780+1690+1680+1740+1700)}{6} = \boxed{\textbf{(E) } 1715}.</math>
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 +
-i_am_suk_at_math_2
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 +
==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
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 +
==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(Faster computation)==
 +
https://youtu.be/l3VrUsZkv8I
 +
 
 +
== 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://youtu.be/uOMi6GISNLg?si=UbAI9jSq52yXNAAV
 +
 
 +
==Video Solution by Just Math⚡==
 +
https://www.youtube.com/watch?v=o1Kiz_lZc90
 +
 
 +
==Video Solution by Dr. David==
 +
https://youtu.be/bJfg7VqyI_I
 +
 
 +
==See Also==
 +
{{AMC10 box|year=2024|ab=A|num-b=11|num-a=13}}
 +
{{MAA Notice}}

Latest revision as of 11:44, 11 June 2025

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?Screenshot 2024-11-08 1.51.51 PM.png

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

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(Faster computation)

https://youtu.be/l3VrUsZkv8I

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://youtu.be/uOMi6GISNLg?si=UbAI9jSq52yXNAAV

Video Solution by Just Math⚡

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

Video Solution by Dr. David

https://youtu.be/bJfg7VqyI_I

See Also

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

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

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