So this is some practice work i have and i was wondering if someone could help me so when i take the test i know how to write out and solve the word problems.
Jason bought 6 movie tickets and 4 bags of popcorn. Michael bought 2 movie tickets and 3 bags of popcorn.Each bag of popcorn was $5 and they spent $131 total.
Part A:First i wanted to ask what this would look like in the form of an equation, and could you define the variable?
Part B: I need to know how to find the cost of each movie ticket, how do i do this?
Part C: After that i would need to check my answer and explain if its reasonable (while showing my work). Then i would need to explain what a unreasonable answer would be.
Part D: Example: Sally buys 8 movie tickets and 5 bags of popcorn. How much will Sally have to pay?
Thank you in advance and god bless
6 t + 4 p + 2 t + 3 p = 131
t = ticket price
and p = popcorn price =$5
which is 8 t + 7 p = 131
so 8 t + 7 * 5 = 131
8 t = 131 - 35 = 96
t = $12 per ticket
Now go back and check using $12 for t and $5 for popcorn
then Sally spends 8*12 + 5*5
Part A: To write the equation, let's define the variables.
Let's say the cost of each movie ticket is "T" and the cost of each bag of popcorn is "P."
Since Jason bought 6 movie tickets and 4 bags of popcorn, his total cost can be represented as follows:
6T + 4P
Similarly, Michael's total cost can be represented as:
2T + 3P
According to the given information, the total cost for both of them is $131. Therefore, we can create the equation:
6T + 4P + 2T + 3P = 131
Part B: To find the cost of each movie ticket, we need to eliminate the variable "P" from the equation. We can do this by combining the terms with "P" and isolating the "T" term on one side of the equation. Rearranging the equation:
6T + 2T + 4P + 3P = 131
8T + 7P = 131
Now, isolate the "T" term:
8T = 131 - 7P
T = (131 - 7P) / 8
Part C: To check if our answer is reasonable, we need to substitute the values of "T" and "P" back into the original equation. For example, let's assume the cost of each bag of popcorn is $5 (P = 5). Using this value, we can calculate the cost of each movie ticket (T) using the equation T = (131 - 7P) / 8.
Substituting the values:
T = (131 - 7*5) / 8
T = (131 - 35) / 8
T = 96 / 8
T = 12
Therefore, the cost of each movie ticket is $12.
To check the reasonableness, substitute the values of T and P into the original equation:
6T + 4P + 2T + 3P = 131
(6*12) + (4*5) + (2*12) + (3*5) = 131
72 + 20 + 24 + 15 = 131
131 = 131
The equation balances, so our answer is reasonable.
An unreasonable answer would occur if, for example, the cost of each movie ticket came out to be a negative value or an extremely high value compared to real-world prices.
Part D: Let's calculate the total cost for Sally:
Given that Sally buys 8 movie tickets and 5 bags of popcorn, we can use the same equation to calculate the total cost:
6T + 4P = ?
Substituting T = 12 (from our previous answer) and P = 5:
6*12 + 4*5 = 72 + 20 = 92
So, Sally will have to pay a total of $92.
Note: In the future, if you have any specific questions or need further explanations, feel free to ask!
Part A:
To represent the given information in the form of an equation, we can define variables for the unknowns. Let's define:
Let x be the cost of each movie ticket.
Let y be the cost of each bag of popcorn.
Since Jason bought 6 movie tickets and 4 bags of popcorn, the total cost for Jason would be:
6x + 4y
Michael bought 2 movie tickets and 3 bags of popcorn, resulting in a total cost for Michael:
2x + 3y
Given that the total cost for both Jason and Michael is $131, we can form the equation:
6x + 4y + 2x + 3y = 131
Part B:
To find the cost of each movie ticket, we can isolate the x variable in the equation.
Combine like terms:
6x + 2x + 4y + 3y = 131
8x + 7y = 131
Now isolate x:
8x = 131 - 7y
Divide both sides by 8:
x = (131 - 7y) / 8
Therefore, the cost of each movie ticket is (131 - 7y) / 8.
Part C:
To check our answer, we can substitute the values of variables back into the equation and verify if it satisfies the original conditions.
Let's assume the cost of each bag of popcorn is $5. Thus, y = 5.
Substitute the value of y into our equation:
8x + 7(5) = 131
8x + 35 = 131
8x = 131 - 35
8x = 96
x = 96 / 8
x = 12
So, the cost of each movie ticket is $12.
To assess if the answer is reasonable, we should consider the given information. The total cost for Jason and Michael combined was $131, and they bought a total of 6 movie tickets. Therefore, the average cost of each ticket would be $21.83 ($131 divided by 6). Since our answer ($12) is much lower than the average, it seems reasonable that Jason and Michael paid a discounted price, perhaps through a promotion or bulk purchase, making it plausible that the answer is correct.
An unreasonable answer, in this case, would be if the cost of each movie ticket turned out to be negative or an excessively high value that does not align with the given information or real-world pricing.
Part D:
To calculate how much Sally will have to pay, we can apply the same approach.
Let's assume the cost of each movie ticket is still x and each bag of popcorn costs y.
Like before, we can set up the equation:
8x + 5y = ?
To find the total cost, we need specific values for x and y. If those are not provided, we won't be able to calculate the exact amount Sally would have to pay.
To determine the total cost, we would need additional information specifying the values of x and y (the cost of the movie ticket and popcorn).