Question

请教初一数学题

1)A group of students are going on a picnic.The total expenditure will be shared equally among all students.If each student pays $65,they will be $300 short.If each student pays $75,they will have an excess of $100.Find the number of students joining the picnic.

2)John's savings is $300 more than his sister's.After giving $450 of his savings to his sister,John's savings becomes 2/5 of his sister's.How much savings do they have altogether?

3)Consider the equation x-2x+3x-4x+5x-6x+...+99x-100x =200. Solve the equation and briefly explain how you can solve it.

Answer 1

1、设学生人数为X
65X+300=75X-100 X=40

或 300+100=400 400/(75-65)=40

2、450-300=150 150+450=600 600/(1-2/5)=1000 1000-450=550 550+300=850
550+850=1400

或设总共有X$
(X+300)/2-450=2/5[(X-300)/2+450] X=1400

3、-50X=200 X=-4
说明： （x-2x）+（3x-4x）+（5x-6x）+...+（99x-100x） =200
-X-X-X-...-X=200
-50X=200
X=-4