I can not find my notes over my distributive property. I know this problem is really easy, I just am not sure where to start!

Question

Solve each of the followng:

2x+5 = 3x-4

Also, this problem. I am not sure where to begin:

For a particular event, 812 tickets were sold for a total of $1912. If students paid $2 per ticket and nonstudents paid $3 per ticket, how many student tickets were sold?

You don't even need the distributive law for the first problem. Remember, you need to get all the variables (x) on one side of the equation, and all numbers on the other side. So, subtract 2x from both sides of the equation. You end up with 5 = x-4. Then add 4 to both sides...9 = x.

For the second problem, you need to set up 2 equations with 2 unknowns. We'll call the amount of student tickets x and the amount of nonstudent tickets y. Since the students paid $2 per ticket, and nonstudents paid $2 per ticket, you can write the equation: 2x + 3y = 1912. Then for the second equuation, you write x + y = 812. So, now we can solve this because we have 2 equations and 2 unknowns.

2x + 3y = 1912
x + y = 812

multiply the botton equation by 2:

2x + 3y = 1912
2x + 2y = 1624

Then subtract the second equation from the first:

y = 288
so, x must by 812 - 288 = 524

Thanks so much Dan. I really am bad with word problems. I have been doing these problems since 3pm and I think I have looked at them too long. Thanks so much for your help!

You're welcome.

Alice has three daughters all of whom are at least one year old.Alice challenged a friend Morag to work out the ages from the following clues:the sum of their ages is 11;the product of their ages is either 16 years less or 16 years more than Morag's age.Morag said she could not identify the ages and would need another clue so Alice said that the daughter whose age in years is greatest is learning to play the clarinet.Morag now knew the three ages.What were they,and how did Morag know ?

They are 1, 2 and 8. But you can work it out for yourself ;-)