Difference between revisions of "2020 AMC 8 Problems"
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==Problem 1== | ==Problem 1== | ||
Luka is making lemonade to sell at a school fundraiser. His recipe requires <math>4</math> times as much water as sugar and twice as much sugar as lemon juice. He uses <math>3</math> cups of lemon juice. How many cups of water does he need? | Luka is making lemonade to sell at a school fundraiser. His recipe requires <math>4</math> times as much water as sugar and twice as much sugar as lemon juice. He uses <math>3</math> cups of lemon juice. How many cups of water does he need? | ||
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<math>\textbf{(A) } 6\qquad\textbf{(B) } 8\qquad\textbf{(C) } 12\qquad\textbf{(D) } 18\qquad\textbf{(E) } 24\qquad</math> | <math>\textbf{(A) } 6\qquad\textbf{(B) } 8\qquad\textbf{(C) } 12\qquad\textbf{(D) } 18\qquad\textbf{(E) } 24\qquad</math> | ||
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| + | [[2020 AMC 8 Problems/Problem 1|Solution]] | ||
| + | |||
| + | ==Problem 2== | ||
| + | Four friends do yardwork for their neighbors over the weekend, earning <math>\$15, \$20, \$25,</math> and <math>\$40,</math> respectively. They decide to split their earnings equally among themselves. In total how much will the friend who earned <math>\$40</math> give to the others? | ||
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| + | [[2020 AMC 8 Problems/Problem 2|Solution]] | ||
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| + | <math>\textbf{(A) }\$5 \qquad \textbf{(B) }\$10 \qquad \textbf{(C) }\$15 \qquad \textbf{(D) }\$20 \qquad \textbf{(E) }\$25</math> | ||
| + | |||
| + | ==Problem 3== | ||
| + | Carrie has a rectangular garden that measures <math>6</math> feet by <math>8</math> feet. She plants the entire garden with strawberry plants. Carrie is able to plant <math>4</math> strawberry plants per square foot, and she harvests an average of <math>10</math> strawberries per plant. How many strawberries can she expect to harvest? | ||
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| + | <math>\textbf{(A) }560 \qquad \textbf{(B) }960 \qquad \textbf{(C) }1120 \qquad \textbf{(D) }1920 \qquad \textbf{(E) }3840</math> | ||
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| + | [[2020 AMC 8 Problems/Problem 3|Solution]] | ||
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| + | ==Problem 4== | ||
| + | Three hexagons of increasing size are shown below. Suppose the dot pattern continues so that each successive hexagon contains one more band of dots. How many dots are in the next hexagon? | ||
| + | <asy> | ||
| + | size(250); | ||
| + | real side1 = 1.5; | ||
| + | real side2 = 4.0; | ||
| + | real side3 = 6.5; | ||
| + | real pos = 2.5; | ||
| + | pair s1 = (-10,-2.19); | ||
| + | pair s2 = (15,2.19); | ||
| + | pen grey1 = rgb(100/256, 100/256, 100/256); | ||
| + | pen grey2 = rgb(183/256, 183/256, 183/256); | ||
| + | fill(circle(origin + s1, 1), grey1); | ||
| + | for (int i = 0; i < 6; ++i) { | ||
| + | draw(side1*dir(60*i)+s1--side1*dir(60*i-60)+s1,linewidth(1.25)); | ||
| + | } | ||
| + | fill(circle(origin, 1), grey1); | ||
| + | for (int i = 0; i < 6; ++i) { | ||
| + | fill(circle(pos*dir(60*i),1), grey2); | ||
| + | draw(side2*dir(60*i)--side2*dir(60*i-60),linewidth(1.25)); | ||
| + | } | ||
| + | fill(circle(origin+s2, 1), grey1); | ||
| + | for (int i = 0; i < 6; ++i) { | ||
| + | fill(circle(pos*dir(60*i)+s2,1), grey2); | ||
| + | fill(circle(2*pos*dir(60*i)+s2,1), grey1); | ||
| + | fill(circle(sqrt(3)*pos*dir(60*i+30)+s2,1), grey1); | ||
| + | draw(side3*dir(60*i)+s2--side3*dir(60*i-60)+s2,linewidth(1.25)); | ||
| + | } | ||
| + | </asy> | ||
| + | |||
| + | [[2020 AMC 8 Problems/Problem 4|Solution]] | ||
| + | |||
| + | <math>\textbf{(A) }35 \qquad \textbf{(B) }37 \qquad \textbf{(C) }39 \qquad \textbf{(D) }43 \qquad \textbf{(E) }49</math> | ||
| + | |||
| + | ==Problem 5== | ||
| + | Three fourths of a pitcher is filled with pineapple juice. The pitcher is emptied by pouring an equal amount of juice into each of <math>5</math> cups. What percent of the total capacity of the pitcher did each cup receive? | ||
| + | |||
| + | <math>\textbf{(A) }5 \qquad \textbf{(B) }10 \qquad \textbf{(C) }15 \qquad \textbf{(D) }20 \qquad \textbf{(E) }25</math> | ||
| + | |||
| + | [[2020 AMC 8 Problems/Problem 5|Solution]] | ||
Revision as of 21:50, 17 November 2020
Problem 1
Luka is making lemonade to sell at a school fundraiser. His recipe requires 
times as much water as sugar and twice as much sugar as lemon juice. He uses 
cups of lemon juice. How many cups of water does he need?
Problem 2
Four friends do yardwork for their neighbors over the weekend, earning 
and 
respectively. They decide to split their earnings equally among themselves. In total how much will the friend who earned 
give to the others?
Problem 3
Carrie has a rectangular garden that measures 
feet by 
feet. She plants the entire garden with strawberry plants. Carrie is able to plant strawberry plants per square foot, and she harvests an average of 
strawberries per plant. How many strawberries can she expect to harvest?
Problem 4
Three hexagons of increasing size are shown below. Suppose the dot pattern continues so that each successive hexagon contains one more band of dots. How many dots are in the next hexagon?
![[asy] size(250); real side1 = 1.5; real side2 = 4.0; real side3 = 6.5; real pos = 2.5; pair s1 = (-10,-2.19); pair s2 = (15,2.19); pen grey1 = rgb(100/256, 100/256, 100/256); pen grey2 = rgb(183/256, 183/256, 183/256); fill(circle(origin + s1, 1), grey1); for (int i = 0; i < 6; ++i) { draw(side1*dir(60*i)+s1--side1*dir(60*i-60)+s1,linewidth(1.25)); } fill(circle(origin, 1), grey1); for (int i = 0; i < 6; ++i) { fill(circle(pos*dir(60*i),1), grey2); draw(side2*dir(60*i)--side2*dir(60*i-60),linewidth(1.25)); } fill(circle(origin+s2, 1), grey1); for (int i = 0; i < 6; ++i) { fill(circle(pos*dir(60*i)+s2,1), grey2); fill(circle(2*pos*dir(60*i)+s2,1), grey1); fill(circle(sqrt(3)*pos*dir(60*i+30)+s2,1), grey1); draw(side3*dir(60*i)+s2--side3*dir(60*i-60)+s2,linewidth(1.25)); } [/asy]](http://latex.artofproblemsolving.com/0/1/2/012deb289407de96d835545a93028e20c35551f7.png)
Problem 5
Three fourths of a pitcher is filled with pineapple juice. The pitcher is emptied by pouring an equal amount of juice into each of 
cups. What percent of the total capacity of the pitcher did each cup receive?
