Ok, these questions were one's that I couldn't figure out how to work. If someone could set me up on how to solve each one it would be great. Thank you!
1. A movie theater had a certain number of tickets to give away. Five people got the tickets. The first got one-third of the tickets, the second got one-fourth of the tickets, and the third got one-fifth of the tickets. The fourth person got eight tickets, and there were five tickets left for the fifth person. Find the total number of tickets given away.
b. About 35.9% of all charitable contributions are made to religious organizations. In 2003, about $86.4 billion was given to religious organizations. How much was given to charities in general?
3. It costs $225 per month plus 1.2¢ per copy to rent a copy machine. A catalog publisher needs to lease a copy machine for use during a special project that they anticipate will take 3 months. They decide to rent the copier, but must stay within a budget of $2400 for copies. Determine (in terms of an inequality) the number of copies they can make and still remain within budget.
( for this one, I think I did it right, and would love for someone to check it for me. If it's wrong, could you tell me what my mistake was?)
4. Simplify. Describe the steps you used to arrive at your final answer.
2(to the 3rd power) - 10[4-(-2+18)3]
I got : 432
TY again.
1. Let x = total number
x - 1/3x -1/4x - 1/5x - 8 = 5
Solve for x.
b(?). 86.4 = .359x (in billions)
3. 3(225) + .012x < 2400, where x = number of copies.
4. x^2 = x squared online. What are you doing with the final 3 in the formula? What is missing?
Sure! I'll walk you through each question and explain how to solve them.
1. To find the total number of movie tickets given away, we need to add up the number of tickets each person received. The first person got one-third of the tickets, the second person got one-fourth, and the third person got one-fifth. The fourth person got eight tickets, and the remaining five tickets were given to the fifth person. To solve this problem, we'll use algebraic expressions.
Let's say the total number of tickets is represented by 'x'. Then:
- The first person got (1/3)x tickets.
- The second person got (1/4)x tickets.
- The third person got (1/5)x tickets.
- The fourth person got 8 tickets.
- The fifth person got 5 tickets.
So, the equation becomes:
(1/3)x + (1/4)x + (1/5)x + 8 + 5 = x
To solve for 'x', we'll combine like terms and isolate 'x':
(20x + 15x + 12x) / 60 + 8 + 5 = x
(47x / 60) + 13 = x
47x = 60x + 780
13x = 780
x = 60
Therefore, the total number of tickets given away is 60.
b. To find out how much was given to charities in general, we can use the percentage given to religious organizations in 2003 and the total amount given to religious organizations that year.
Let's assume the total amount given to charities in general is represented by 'y'. Then, we can set up a proportion using the given information:
(35.9/100) = (86.4/y)
To solve for 'y':
Cross multiply: 35.9 * y = 100 * 86.4
35.9y = 8640
y = 8640/35.9
y ≈ $240.67 billion
Therefore, approximately $240.67 billion was given to charities in general in 2003.
3. To find the number of copies the catalog publisher can make while staying within the budget, we need to set up an inequality.
Let's assume the number of copies made is represented by 'c'. The cost for renting the copy machine is $225 per month plus 1.2¢ (0.012 dollars) per copy. So the total cost 'T' for 'c' copies made over 'm' months is given by:
T = 225m + 0.012c
We know that the project will take 3 months, and the budget is $2400. So the inequality becomes:
225(3) + 0.012c ≤ 2400
675 + 0.012c ≤ 2400
To solve for 'c':
0.012c ≤ 2400 - 675
0.012c ≤ 1725
c ≤ 1725 / 0.012
c ≤ 143750
Therefore, the publisher can make a maximum of 143,750 copies and still remain within budget.
4. Let's simplify the expression step by step:
2^(3) - 10[4 - (-2 + 18) * 3]
1. Start by simplifying the innermost parentheses:
2^(3) - 10[4 - 16 * 3]
2. Perform the multiplication inside the square brackets:
2^(3) - 10[4 - 48]
3. Subtract inside the square brackets:
2^(3) - 10[-44]
4. Perform the exponentiation:
8 - 10[-44]
5. Multiply -10 by -44:
8 + 440
6. Add the two numbers together:
448
Therefore, the simplified expression is 448.
I hope this helps! Let me know if you have any further questions or need further clarification.