I have this math project and I'm stumped on this word problem. Any point in the right direction would be greatly appreciated..
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.
You'll have to set up an equation to model this situation. Let t be the total number of tickets, and see what you can come up with. (Hint: The word "of" is the same as "multiplied by.")
I think I got it...so the equation would look like 1/3(t)+1/4(t)+1/5(t)+8+5=total #??
Right, but don't forget that t is our total number of tickets, so it should be...
1/3(t)+1/4(t)+1/5(t)+8+5 = t
Then, solve for t. If you have any more questions, I'll be glad to help.
Okay so after isolating "t" on one side of the equation I came up with
47/60(t)=t-13...after subtracting "t"...I got
-13/60(t)=-13..after doing the division found out t=60!..think its right because I plugged it back into my orginal equation and found 1/4,1/5/,1/3 plus 8 and 5 equals 60...did I get it right?!
That's right. There were 60 tickets. Good job! :)
To solve this word problem, let's break it down step by step.
1. Let's start by assigning variables to the unknown quantities.
- Let's say the total number of tickets given away is "T".
- We can assign a variable like "x" to represent the number of tickets initially available.
2. We know from the problem that the first person got one third of the tickets. This can be expressed as:
- First person: x/3
3. The second person got one fourth of the tickets:
- Second person: x/4
4. The third person got one fifth of the tickets:
- Third person: x/5
5. The fourth person got 8 tickets, and there were 5 tickets left for the fifth person. This means:
- Fourth person: 8
- Fifth person: 5
6. Now, let's set up an equation to represent the information given in the problem:
- x/3 + x/4 + x/5 + 8 + 5 = T
7. To solve for "x", we need to find a common denominator for the fractions in the equation. The least common multiple of 3, 4, and 5 is 60:
- (20x + 15x + 12x)/60 + 8 + 5 = T
- (47x + 60)/60 + 13 = T
8. Simplify the equation:
- (47x + 60 + 13 * 60)/60 = T
- (47x + 60 + 780)/60 = T
- (47x + 840)/60 = T
9. Now, let's solve for "x" by isolating it on one side of the equation:
- 47x + 840 = 60T
- 47x = 60T - 840
- x = (60T - 840)/47
10. Since we want to find the total number of tickets given away, T, we need to substitute the value we found for "x" into the equation for "T":
- T = (47(60T - 840))/47
- T = 60T - 840
11. Solve for "T":
- 840 = 59T
- T = 840/59
- T ≈ 14.24
Therefore, the total number of tickets given away is approximately 14.24. However, since tickets cannot be fractional, we can conclude that the theater gave away 14 tickets in total.