Difference between revisions of "2000 AMC 8 Problems/Problem 4"
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+ | ==Problem== | ||
+ | |||
+ | In 1960 only 5% of the working adults in Carlin City worked | ||
+ | at home. By 1970 the "at-home" work force had increased to | ||
+ | 8%. In 1980 there were approximately 15% working at home, | ||
+ | and in 1990 there were 30%. The graph that best illustrates | ||
+ | this is: | ||
+ | |||
+ | <asy> | ||
+ | unitsize(18); | ||
+ | |||
+ | draw((0,4)--(0,0)--(7,0)); | ||
+ | draw((0,1)--(.2,1)); draw((0,2)--(.2,2)); draw((0,3)--(.2,3)); | ||
+ | draw((2,0)--(2,.2)); draw((4,0)--(4,.2)); draw((6,0)--(6,.2)); | ||
+ | for (int a = 1; a < 4; ++a) | ||
+ | { | ||
+ | for (int b = 1; b < 4; ++b) | ||
+ | { | ||
+ | draw((2*a,b-.1)--(2*a,b+.1)); | ||
+ | draw((2*a-.1,b)--(2*a+.1,b)); | ||
+ | } | ||
+ | } | ||
+ | label("1960",(0,0),S); label("1970",(2,0),S); label("1980",(4,0),S); label("1990",(6,0),S); | ||
+ | label("10",(0,1),W); label("20",(0,2),W); label("30",(0,3),W); | ||
+ | label("$\%$",(0,4),N); | ||
+ | |||
+ | draw((12,4)--(12,0)--(19,0)); | ||
+ | draw((12,1)--(12.2,1)); draw((12,2)--(12.2,2)); draw((12,3)--(12.2,3)); | ||
+ | draw((14,0)--(14,.2)); draw((16,0)--(16,.2)); draw((18,0)--(18,.2)); | ||
+ | for (int a = 1; a < 4; ++a) | ||
+ | { | ||
+ | for (int b = 1; b < 4; ++b) | ||
+ | { | ||
+ | draw((2*a+12,b-.1)--(2*a+12,b+.1)); | ||
+ | draw((2*a+11.9,b)--(2*a+12.1,b)); | ||
+ | } | ||
+ | } | ||
+ | label("1960",(12,0),S); label("1970",(14,0),S); label("1980",(16,0),S); label("1990",(18,0),S); | ||
+ | label("10",(12,1),W); label("20",(12,2),W); label("30",(12,3),W); | ||
+ | label("$\%$",(12,4),N); | ||
+ | |||
+ | draw((0,12)--(0,8)--(7,8)); | ||
+ | draw((0,9)--(.2,9)); draw((0,10)--(.2,10)); draw((0,11)--(.2,11)); | ||
+ | draw((2,8)--(2,8.2)); draw((4,8)--(4,8.2)); draw((6,8)--(6,8.2)); | ||
+ | for (int a = 1; a < 4; ++a) | ||
+ | { | ||
+ | for (int b = 1; b < 4; ++b) | ||
+ | { | ||
+ | draw((2*a,b+7.9)--(2*a,b+8.1)); | ||
+ | draw((2*a-.1,b+8)--(2*a+.1,b+8)); | ||
+ | } | ||
+ | } | ||
+ | label("1960",(0,8),S); label("1970",(2,8),S); label("1980",(4,8),S); label("1990",(6,8),S); | ||
+ | label("10",(0,9),W); label("20",(0,10),W); label("30",(0,11),W); | ||
+ | label("$\%$",(0,12),N); | ||
+ | |||
+ | draw((12,12)--(12,8)--(19,8)); | ||
+ | draw((12,9)--(12.2,9)); draw((12,10)--(12.2,10)); draw((12,11)--(12.2,11)); | ||
+ | draw((14,8)--(14,8.2)); draw((16,8)--(16,8.2)); draw((18,8)--(18,8.2)); | ||
+ | for (int a = 1; a < 4; ++a) | ||
+ | { | ||
+ | for (int b = 1; b < 4; ++b) | ||
+ | { | ||
+ | draw((2*a+12,b+7.9)--(2*a+12,b+8.1)); | ||
+ | draw((2*a+11.9,b+8)--(2*a+12.1,b+8)); | ||
+ | } | ||
+ | } | ||
+ | label("1960",(12,8),S); label("1970",(14,8),S); label("1980",(16,8),S); label("1990",(18,8),S); | ||
+ | label("10",(12,9),W); label("20",(12,10),W); label("30",(12,11),W); | ||
+ | label("$\%$",(12,12),N); | ||
+ | |||
+ | draw((24,12)--(24,8)--(31,8)); | ||
+ | draw((24,9)--(24.2,9)); draw((24,10)--(24.2,10)); draw((24,11)--(24.2,11)); | ||
+ | draw((26,8)--(26,8.2)); draw((28,8)--(28,8.2)); draw((30,8)--(30,8.2)); | ||
+ | for (int a = 1; a < 4; ++a) | ||
+ | { | ||
+ | for (int b = 1; b < 4; ++b) | ||
+ | { | ||
+ | draw((2*a+24,b+7.9)--(2*a+24,b+8.1)); | ||
+ | draw((2*a+23.9,b+8)--(2*a+24.1,b+8)); | ||
+ | } | ||
+ | } | ||
+ | label("1960",(24,8),S); label("1970",(26,8),S); label("1980",(28,8),S); label("1990",(30,8),S); | ||
+ | label("10",(24,9),W); label("20",(24,10),W); label("30",(24,11),W); | ||
+ | label("$\%$",(24,12),N); | ||
+ | |||
+ | draw((0,9)--(2,9.25)--(4,10)--(6,11)); | ||
+ | draw((12,8.5)--(14,9)--(16,10)--(18,10.5)); | ||
+ | draw((24,8.5)--(26,8.8)--(28,10.5)--(30,11)); | ||
+ | draw((0,0.5)--(2,1)--(4,2.8)--(6,3)); | ||
+ | draw((12,0.5)--(14,.8)--(16,1.5)--(18,3)); | ||
+ | |||
+ | label("(A)",(-1,12),W); | ||
+ | label("(B)",(11,12),W); | ||
+ | label("(C)",(23,12),W); | ||
+ | label("(D)",(-1,4),W); | ||
+ | label("(E)",(11,4),W); | ||
+ | </asy> | ||
+ | |||
+ | |||
+ | ==Solution== | ||
+ | |||
The data are <math>1960 (5\%)</math>, <math>1970 (8\%)</math>, <math>1980 (15\%)</math>, and <math>1990 (30\%)</math>. Only one of these graphs has the answer and that is choice <math>\boxed{E}</math>. | The data are <math>1960 (5\%)</math>, <math>1970 (8\%)</math>, <math>1980 (15\%)</math>, and <math>1990 (30\%)</math>. Only one of these graphs has the answer and that is choice <math>\boxed{E}</math>. | ||
+ | |||
+ | ==See Also== | ||
+ | |||
+ | {{AMC8 box|year=2000|num-b=3|num-a=5}} |
Revision as of 09:09, 15 May 2011
Problem
In 1960 only 5% of the working adults in Carlin City worked at home. By 1970 the "at-home" work force had increased to 8%. In 1980 there were approximately 15% working at home, and in 1990 there were 30%. The graph that best illustrates this is:
Solution
The data are , , , and . Only one of these graphs has the answer and that is choice .
See Also
2000 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
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 AJHSME/AMC 8 Problems and Solutions |