Question

18．某學校六年級甲、乙、丙三個班向災區(qū)捐款，甲班捐的錢數(shù)是其余兩班的$\frac{2}{3}$，乙班捐的錢數(shù)是其余兩班之和的$\frac{2}{5}$，如果甲班與乙班共捐款144元，丙班捐款了多少元？

Answer 1

分析 設甲班捐款了x元，則乙班捐了144-x元，甲班捐的錢數(shù)是其余兩班的$\frac{2}{3}$，可得甲班捐的錢數(shù)是三班的$\frac{2}{5}$，乙班捐的錢數(shù)是其余兩班之和的$\frac{2}{5}$，可得乙班捐的錢數(shù)是三班的$\frac{2}{7}$，根據(jù)等量關系：甲班捐的錢數(shù)÷$\frac{2}{5}$=乙班捐的錢數(shù)÷$\frac{2}{7}$，列方程解答即可的甲班捐的款數(shù)，再求丙班捐款了多少元．

解答 解：設甲班捐款了x元，則乙班捐了144-x元，甲班捐的錢數(shù)是其余兩班的$\frac{2}{3}$，可得甲班捐的錢數(shù)是三班的$\frac{2}{5}$，乙班捐的錢數(shù)是其余兩班之和的$\frac{2}{5}$，可得乙班捐的錢數(shù)是三班的$\frac{2}{7}$，
x÷$\frac{2}{5}$=（144-x）÷$\frac{2}{7}$
  $\frac{5}{2}$x=504-$\frac{7}{2}$x
  6x=504
   x=84
84÷$\frac{2}{5}$-144
=210-144
=66（元）
答：丙班捐款了66元．

點評 本題考查了分數(shù)四則復合應用題，關鍵是根據(jù)等量關系：甲班捐的錢數(shù)÷$\frac{2}{5}$=乙班捐的錢數(shù)÷$\frac{2}{7}$，列方程．