73. train tickets at the pittsburgh zoo, children ride a train for 25 cents, adults pay $1.00, and senior…

73. train tickets at the pittsburgh zoo, children ride a train for 25 cents, adults pay $1.00, and senior citizens 75 cents. on a given day, 1400 passengers paid a total of $740 for the rides. there were 250 more children riders than all other riders. find the number of children, adult, and senior riders.

73. train tickets at the pittsburgh zoo, children ride a train for 25 cents, adults pay $1.00, and senior citizens 75 cents. on a given day, 1400 passengers paid a total of $740 for the rides. there were 250 more children riders than all other riders. find the number of children, adult, and senior riders.

Answer

Explanation:

Step1: Definir variables

Sea ( x ) el número de niños, ( y ) el número de adultos y ( z ) el número de ancianos. Tenemos que ( x + y+ z=1400 ) y ( x=y + z + 250 ). Sustituyendo ( x ) en la primera ecuación: ( (y + z + 250)+y + z=1400 ), lo que simplifica a ( 2y + 2z=1150 ) o ( y + z = 575 ), entonces ( x=1400-(y + z)=1400 - 575=825 ). El costo total es ( 0.25x+y + 0.75z=740 ). Sustituyendo ( x = 825 ) en la ecuación de costo: ( 0.25\times825+y + 0.75z=740 ), ( 206.25+y + 0.75z=740 ), ( y + 0.75z=533.75 ). Como ( y=575 - z ), sustituimos: ( 575 - z+0.75z=533.75 ), ( - 0.25z=533.75 - 575 ), ( - 0.25z=-41.25 ), ( z = 165 ).

Step2: Calcular ( y )

Como ( y + z=575 ) y ( z = 165 ), entonces ( y=575 - 165 = 410 ).

Answer:

Número de niños: ( 825 ), número de adultos: ( 410 ), número de ancianos: ( 165 ).