2024 AMC 10A Problems/Problem 12: Difference between revisions

Latest revision as of 10:58, 2 November 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?

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

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 $1700 + \frac{80-10-20+40+0}{6} = \boxed{\textbf{(E) }1715}$ .

Sidenote: Many people would just add up the changes, which would give them 1700. That is wrong.

-mathfun2012

-JK2030 minor edit

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

Solution 4

Plugging in x as 1700, we get the variables as: x + 80, x-10, x-20, x+40, and x. Finding the average of this gets us (6x + 90)/6 = x + 15 Since x is 1700 we get our answer as 1700 + 15 = $\boxed{\textbf{(E) }1715}$

~Ninjago_342

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

Video solution by TheNeuralMathAcademy

https://www.youtube.com/watch?v=4b_YLnyegtw&t=1904s

@@ Line 1: / Line 1: @@
-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."
+==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>.
+Sidenote: Many people would just add up the changes, which would give them 1700. That is wrong.
+-mathfun2012
+-JK2030 minor edit
+==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
+==Solution 4==
+Plugging in x as 1700, we get the variables as: x + 80, x-10, x-20, x+40, and x.
+Finding the average of this gets us (6x + 90)/6 = x + 15
+Since x is 1700 we get our answer as 1700 + 15 = <math>\boxed{\textbf{(E) }1715}</math>
+~Ninjago_342
+==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
+== Video solution by TheNeuralMathAcademy ==
+https://www.youtube.com/watch?v=4b_YLnyegtw&t=1904s
+==See Also==
+{{AMC10 box|year=2024|ab=A|before=[[2023 AMC 10B Problems]]|after=[[2024 AMC 10B Problems]]}}
+* [[AMC 10]]
+* [[AMC 10 Problems and Solutions]]
+* [[Mathematics competitions]]
+* [[Mathematics competition resources]]
+{{MAA Notice}}

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