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: @@
-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>.
+-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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