# 1991 AJHSME Problems/Problem 18

## Problem

The vertical axis indicates the number of employees, but the scale was accidentally omitted from this graph. What percent of the employees at the Gauss company have worked there for $5$ years or more? $[asy] for(int a=1; a<11; ++a) { draw((a,0)--(a,-.5)); } draw((0,10.5)--(0,0)--(10.5,0)); label("1",(1,-.5),S); label("2",(2,-.5),S); label("3",(3,-.5),S); label("4",(4,-.5),S); label("5",(5,-.5),S); label("6",(6,-.5),S); label("7",(7,-.5),S); label("8",(8,-.5),S); label("9",(9,-.5),S); label("10",(10,-.5),S); label("Number of years with company",(5.5,-2),S); label("X",(1,0),N); label("X",(1,1),N); label("X",(1,2),N); label("X",(1,3),N); label("X",(1,4),N); label("X",(2,0),N); label("X",(2,1),N); label("X",(2,2),N); label("X",(2,3),N); label("X",(2,4),N); label("X",(3,0),N); label("X",(3,1),N); label("X",(3,2),N); label("X",(3,3),N); label("X",(3,4),N); label("X",(3,5),N); label("X",(3,6),N); label("X",(3,7),N); label("X",(4,0),N); label("X",(4,1),N); label("X",(4,2),N); label("X",(5,0),N); label("X",(5,1),N); label("X",(6,0),N); label("X",(6,1),N); label("X",(7,0),N); label("X",(7,1),N); label("X",(8,0),N); label("X",(9,0),N); label("X",(10,0),N); label("Gauss Company",(5.5,10),N); [/asy]$ $\text{(A)}\ 9\% \qquad \text{(B)}\ 23\frac{1}{3}\% \qquad \text{(C)}\ 30\% \qquad \text{(D)}\ 42\frac{6}{7}\% \qquad \text{(E)}\ 50\%$

## Solution

Let $x$ be the amount of people each $\text{X}$ represents. The percent of people that worked for five or more years is then $$\frac{2x+2x+2x+x+x+x}{5x+5x+8x+3x+2x+2x+2x+x+x+x}=30\% \rightarrow \boxed{\text{C}}.$$

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 