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!
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 ;-)
To solve this problem, we need to use a combination of deduction and trial and error. Let's break down the clues:
1. The sum of their ages is 11.
2. The product of their ages is either 16 years less or 16 years more than Morag's age.
3. The daughter whose age is greatest is learning to play the clarinet.
Let's start by listing all the possible combinations of ages that add up to 11:
- 1 + 1 + 9 = 11
- 1 + 2 + 8 = 11
- 1 + 3 + 7 = 11
- 1 + 4 + 6 = 11
- 1 + 5 + 5 = 11
- 2 + 2 + 7 = 11
- 2 + 3 + 6 = 11
- 2 + 4 + 5 = 11
- 3 + 3 + 5 = 11
Now, let's go through each of these combinations and check the second clue. We'll assume Morag's age is X:
- 1 + 1 + 9 = 11, which is a product of 9 and 1. This satisfies the second clue.
- 1 + 2 + 8 = 11, which is a product of 16 and 2. This satisfies the second clue.
- 1 + 3 + 7 = 11, which is a product of 21 and 3. This does not satisfy the second clue.
- 1 + 4 + 6 = 11, which is a product of 24 and 4. This does not satisfy the second clue.
- 1 + 5 + 5 = 11, which is a product of 25 and 5. This does not satisfy the second clue.
- 2 + 2 + 7 = 11, which is a product of 28 and 2. This does not satisfy the second clue.
- 2 + 3 + 6 = 11, which is a product of 36 and 3. This does not satisfy the second clue.
- 2 + 4 + 5 = 11, which is a product of 40 and 4. This does not satisfy the second clue.
- 3 + 3 + 5 = 11, which is a product of 45 and 3. This does not satisfy the second clue.
Based on the second clue, we can see that only the combinations (1, 1, 9) and (1, 2, 8) satisfy the condition.
Now, let's look at the third clue. Alice says that the daughter whose age is greatest is learning to play the clarinet. From the previous combinations, we can see that the ages (1, 1, 9) do not satisfy this condition, as the daughter with age 9 is not the oldest. However, the ages (1, 2, 8) do satisfy this condition, as the daughter with age 8 is the oldest.
Therefore, the ages of the three daughters are 1, 2, and 8, and Morag was able to deduce this by using the second clue and the additional information about the clarinet.