Sender: "gayla werry"
My child is in the 6th grade and we are having difficulty with this question. Could you please help us. Thank you.
You have $1.00 to take 100 people to the movies. It costs: 1 cent for 10 children, 3 cents for each woman, 5 cents for each man. You have to take at least one of each category of people. Your answer has to add up to exactly 100 people and exactly $1.00. How many men, women, and children can you take?
Suppose that you have the required collection of people. Put them into three categories, the men, the women and put the children in groups of 10. Suppose the number of men is m, the number of women is w and the number of groups of 10 children is g. There are two conditions to satisfy
If m=19 then the 19 men pay 19*5=95 cents so, from the second condition, g + 3w = 5 cents. Hence w must be 1 and g must be 2. But g=2, w=3 and m=19 does not satisfy the first condition. Thus m is not 19.
If m=18 then the 18 men pay 18*5=90 cents. The two conditions are then
Not to give up lets try m=17. The 17 men then pay 5*17=85 cents and the two conditions become
Now try m=16.