Answer to Question #34047 in Math for annalet

Question

A storekeeper bought three grades of pencils at P2.00, P3.00 and P4.00 a dozen respectively, if he paid a total of P76.50 for them, and bought the same number of each grade, how many pencil did he buy?

Answer 1

A dozen pencils of the first, the second and the third grades is worth P2.00, P3.00, and P4.00 respectively, hence a pencil of the first, the second and the third grades is worth P2.00/12, P3.00/12, and P4.00/12 respectively. The number of each grade is the same, denote it by x. The storekeeper paid a total of P76.50 for them. Thus, 2x/12+3x/12+4x/12=76.50, collect similar terms and obtain 9x/12=76.50. Finally multiply by 12 and divide by 9: x=12*76.50/9=102 pencils, hence the total number of pencils is 3x=3*102=306

Answer: 306 pencils.