Posted by **Kathy** on Tuesday, May 18, 2010 at 8:47pm.

Tickets to a benefit are priced as follows: children $0.50, men $2.00, and women $3.00.

Find one combination in which 100 people may purchase tickets for $100. Children, men and women have to attend the event.

- Math -
**Ashley**, Tuesday, May 18, 2010 at 8:54pm
first multiply 3 by 30 to get 90. if 30 women go, that is $90, so you have to make $10 on men and children, so have 3 men go to get $6 more, and then you need $4 so divide that by $.50 and you get 8, so 8 children have to go.

so you now have 30 women, 3 men, and 6 children.

check your work.

30 x $3 = $90

3 x $2 = $6

8 x $.50= $4

90+6+4=100

does it work?

~aShLeY

- Math -
**Reiny**, Tuesday, May 18, 2010 at 9:06pm
let the number of children be c

let the number of men be m

then the number of women = 100-c-m

(1/2)c + 2m + 3(100-c-m) = 100

c + 4m + 6(100-c-m) = 200

c + 4m + 600 - 6c - 6m = 200

-5c - 2m = -400

2m + 5c = 400

2m = 400 - 5c

m = 200 - (5/2)c , where c > 40 or else m is > 100

now pick any even value of c

e.g. c = 50

m= 200-125 = 75 , no good since we are already over 100

let c = 70

m = 200-(5/2)(70) = 25

w = 100-25-70 = 5

so 70 children, 25 men and 5 women

let c = 72

m = 20

w = 8

See if you can find some others.

remember, the sum cannot exceed 100 people.

- for Ashley - Math -
**Reiny**, Tuesday, May 18, 2010 at 9:16pm
your answer of 30 women, 3 men and 6 children does not add up to 100 people.

- Math -
**Kathy**, Tuesday, May 18, 2010 at 9:39pm
Another way could be

78 children

14 women

8 men

Now how can I explain this to an eight year old?

- Math -
**Reiny**, Tuesday, May 18, 2010 at 9:46pm
Sorry Kathy, your last answer does not work

It satisfies the 100 people condition but does not satisfy the $100 condition.

78(.50) + 14(3) + 8(2) = $97

The only way other than just guessing and checking is to set up equations like I did above.

How to explain this to an eight-year old ????

Wow, you got me there.

- Math -
**Kathy**, Tuesday, May 18, 2010 at 9:55pm
Thanks for your help!

- Math -
**Kathy**, Tuesday, May 18, 2010 at 9:56pm
Thanks for your help, Reiny!

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