Difference between revisions of "2010 AMC 8 Problems/Problem 3"
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https://youtu.be/EEbksvfujhk | https://youtu.be/EEbksvfujhk | ||
| + | ==Video Solution by WhyMath== | ||
| + | https://youtu.be/ra1A86-EoAY | ||
Revision as of 10:23, 18 November 2024
Problem
The graph shows the price of five gallons of gasoline during the first ten months of the year. By what percent is the highest price more than the lowest price?
![[asy] import graph; size(16.38cm); real lsf=2; pathpen=linewidth(0.7); pointpen=black; pen fp = fontsize(10); pointfontpen=fp; real xmin=-1.33,xmax=11.05,ymin=-9.01,ymax=-0.44; pen ycycyc=rgb(0.55,0.55,0.55); pair A=(1,-6), B=(1,-2), D=(1,-5.8), E=(1,-5.6), F=(1,-5.4), G=(1,-5.2), H=(1,-5), J=(1,-4.8), K=(1,-4.6), L=(1,-4.4), M=(1,-4.2), N=(1,-4), P=(1,-3.8), Q=(1,-3.6), R=(1,-3.4), S=(1,-3.2), T=(1,-3), U=(1,-2.8), V=(1,-2.6), W=(1,-2.4), Z=(1,-2.2), E_1=(1.4,-2.6), F_1=(1.8,-2.6), O_1=(14,-6), P_1=(14,-5), Q_1=(14,-4), R_1=(14,-3), S_1=(14,-2), C_1=(1.4,-6), D_1=(1.8,-6), G_1=(2.4,-6), H_1=(2.8,-6), I_1=(3.4,-6), J_1=(3.8,-6), K_1=(4.4,-6), L_1=(4.8,-6), M_1=(5.4,-6), N_1=(5.8,-6), T_1=(6.4,-6), U_1=(6.8,-6), V_1=(7.4,-6), W_1=(7.8,-6), Z_1=(8.4,-6), A_2=(8.8,-6), B_2=(9.4,-6), C_2=(9.8,-6), D_2=(10.4,-6), E_2=(10.8,-6), L_2=(2.4,-3.2), M_2=(2.8,-3.2), N_2=(3.4,-4), O_2=(3.8,-4), P_2=(4.4,-3.6), Q_2=(4.8,-3.6), R_2=(5.4,-3.6), S_2=(5.8,-3.6), T_2=(6.4,-3.4), U_2=(6.8,-3.4), V_2=(7.4,-3.8), W_2=(7.8,-3.8), Z_2=(8.4,-2.8), A_3=(8.8,-2.8), B_3=(9.4,-3.2), C_3=(9.8,-3.2), D_3=(10.4,-3.8), E_3=(10.8,-3.8); filldraw(C_1--E_1--F_1--D_1--cycle,ycycyc); filldraw(G_1--L_2--M_2--H_1--cycle,ycycyc); filldraw(I_1--N_2--O_2--J_1--cycle,ycycyc); filldraw(K_1--P_2--Q_2--L_1--cycle,ycycyc); filldraw(M_1--R_2--S_2--N_1--cycle,ycycyc); filldraw(T_1--T_2--U_2--U_1--cycle,ycycyc); filldraw(V_1--V_2--W_2--W_1--cycle,ycycyc); filldraw(Z_1--Z_2--A_3--A_2--cycle,ycycyc); filldraw(B_2--B_3--C_3--C_2--cycle,ycycyc); filldraw(D_2--D_3--E_3--E_2--cycle,ycycyc); D(B--A,linewidth(0.4)); D(H--(8,-5),linewidth(0.4)); D(N--(8,-4),linewidth(0.4)); D(T--(8,-3),linewidth(0.4)); D(B--(8,-2),linewidth(0.4)); D(B--S_1); D(T--R_1); D(N--Q_1); D(H--P_1); D(A--O_1); D(C_1--E_1); D(E_1--F_1); D(F_1--D_1); D(D_1--C_1); D(G_1--L_2); D(L_2--M_2); D(M_2--H_1); D(H_1--G_1); D(I_1--N_2); D(N_2--O_2); D(O_2--J_1); D(J_1--I_1); D(K_1--P_2); D(P_2--Q_2); D(Q_2--L_1); D(L_1--K_1); D(M_1--R_2); D(R_2--S_2); D(S_2--N_1); D(N_1--M_1); D(T_1--T_2); D(T_2--U_2); D(U_2--U_1); D(U_1--T_1); D(V_1--V_2); D(V_2--W_2); D(W_2--W_1); D(W_1--V_1); D(Z_1--Z_2); D(Z_2--A_3); D(A_3--A_2); D(A_2--Z_1); D(B_2--B_3); D(B_3--C_3); D(C_3--C_2); D(C_2--B_2); D(D_2--D_3); D(D_3--E_3); D(E_3--E_2); D(E_2--D_2); label("0",(0.88,-5.91),SE*lsf,fp); label(" 5",(0.3,-4.84),SE*lsf,fp); label(" 10",(0.2,-3.84),SE*lsf,fp); label(" 15",(0.2,-2.85),SE*lsf,fp); label(" 20",(0.2,-1.85),SE*lsf,fp); label("$\mathrm{Price}$",(0.16,-3.45),SE*lsf,fp); label("$1$",(1.54,-5.97),SE*lsf,fp); label("$2$",(2.53,-5.95),SE*lsf,fp); label("$3$",(3.53,-5.94),SE*lsf,fp); label("$4$",(4.55,-5.94),SE*lsf,fp); label("$5$",(5.49,-5.95),SE*lsf,fp); label("$6$",(6.53,-5.95),SE*lsf,fp); label("$7$",(7.55,-5.95),SE*lsf,fp); label("$8$",(8.52,-5.95),SE*lsf,fp); label("$9$",(9.57,-5.97),SE*lsf,fp); label("$10$",(10.56,-5.94),SE*lsf,fp); label("Month",(7.14,-6.43),SE*lsf,fp); D(A,linewidth(1pt)); D(B,linewidth(1pt)); D(D,linewidth(1pt)); D(E,linewidth(1pt)); D(F,linewidth(1pt)); D(G,linewidth(1pt)); D(H,linewidth(1pt)); D(J,linewidth(1pt)); D(K,linewidth(1pt)); D(L,linewidth(1pt)); D(M,linewidth(1pt)); D(N,linewidth(1pt)); D(P,linewidth(1pt)); D(Q,linewidth(1pt)); D(R,linewidth(1pt)); D(S,linewidth(1pt)); D(T,linewidth(1pt)); D(U,linewidth(1pt)); D(V,linewidth(1pt)); D(W,linewidth(1pt)); D(Z,linewidth(1pt)); D(E_1,linewidth(1pt)); D(F_1,linewidth(1pt)); D(O_1,linewidth(1pt)); D(P_1,linewidth(1pt)); D(Q_1,linewidth(1pt)); D(R_1,linewidth(1pt)); D(S_1,linewidth(1pt)); D(C_1,linewidth(1pt)); D(D_1,linewidth(1pt)); D(G_1,linewidth(1pt)); D(H_1,linewidth(1pt)); D(I_1,linewidth(1pt)); D(J_1,linewidth(1pt)); D(K_1,linewidth(1pt)); D(L_1,linewidth(1pt)); D(M_1,linewidth(1pt)); D(N_1,linewidth(1pt)); D(T_1,linewidth(1pt)); D(U_1,linewidth(1pt)); D(V_1,linewidth(1pt)); D(W_1,linewidth(1pt)); D(Z_1,linewidth(1pt)); D(A_2,linewidth(1pt)); D(B_2,linewidth(1pt)); D(C_2,linewidth(1pt)); D(D_2,linewidth(1pt)); D(E_2,linewidth(1pt)); D(L_2,linewidth(1pt)); D(M_2,linewidth(1pt)); D(N_2,linewidth(1pt)); D(O_2,linewidth(1pt)); D(P_2,linewidth(1pt)); D(Q_2,linewidth(1pt)); D(R_2,linewidth(1pt)); D(S_2,linewidth(1pt)); D(T_2,linewidth(1pt)); D(U_2,linewidth(1pt)); D(V_2,linewidth(1pt)); D(W_2,linewidth(1pt)); D(Z_2,linewidth(1pt)); D(A_3,linewidth(1pt)); D(B_3,linewidth(1pt)); D(C_3,linewidth(1pt)); D(D_3,linewidth(1pt)); D(E_3,linewidth(1pt)); clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle);[/asy]](http://latex.artofproblemsolving.com/3/a/4/3a4bdb0927cad9cd3c3e6a0095656c1113feb8d4.png)
Solution
The highest price was in Month 1, which was $17. The lowest price was in Month 3, which was $10. 17 is 
of 10, and is 
more than 10.
Therefore, the answer is 
Video by MathTalks
Video Solution by WhyMath
See Also
| 2010 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 2 |
Followed by Problem 4 | |
| 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
