Answer:
(a) B
(b) $2
Step-by-step explanation:
(a) Let's say the cost of a ticket is t and the cost of popcorn is p. Then we can write the two equations from the table:
12t + 8p = 184
9t + 6p = 138
We need to solve this, so let's use elimination. Multiply the first equation by 3 and the second equation by 4:
3 * (12t + 8p = 184)
4 * (9t + 6p = 138)
We get:
36t + 24p = 552
36t + 24p = 552
Subtract the second from the first:
36t + 24p = 552
- 36t + 24p = 552
________________
0 = 0
Since we get down to 0 = 0, which is always true, we know that we cannot determine the cost of each ticket because there is more than one solution (infinitely many, actually). The answer is B.
(b) Our equation from this, if we still use t and p, is:
5t + 4p = 82
Now, just choose any of the two equations from above. Let's just pick 9t + 6p = 138. Now, we have the system:
5t + 4p = 82
9t + 6p = 138
To solve, let's use elimination again. Multiply the first equation by 6 and the second one by 4:
6 * (5t + 4p = 82)
4 * (9t + 6p = 138)
We get:
30t + 24p = 492
36t + 24p = 552
Subtract the second from the first:
36t + 24p = 552
- 30t + 24p = 492
________________
6t + 0p = 60
So, t = 60/6 = $10. Plug this back into any of the equations to solve for p:
5t + 4p = 82
5 * 10 + 4p = 82
50 + 4p = 82
4p = 32
p = 32/4 = $8
So the ticket costs 10 - 8 = $2 more dollars than the popcorn.
Answer:
1. 458 - 247 = 211
2. 58.92 - 43.87 = 15.05
3. 51/8 - 15/8 = 4.5
Here you go ! Hope this helps !
Answer:
The cost of chocolate pumpkins is $1.89, masks cost $5.75 and candy witches cost $1.62
Step-by-step explanation:
Let x represent the cost of chocolate pumpkins, y the cost of masks and z the cost of candy witches.
Cory shopping can be represented as:
3x + 4y + 8z = 41.63 (1)
Josh shopping can be represented as:
6x + 2y + 14z = 45.52 (2)
Dan shopping can be represented as:
8x + 3y + 25z = 72.87 (3)
The equations in matrix form is:
![\left[\begin{array}{ccc}3&4&8\\6&2&14\\8&3&25\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{c}41.63\\45.52\\72.87\end{array}\right] \\\\\\\left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}3&4&8\\6&2&14\\8&3&25\end{array}\right] ^{-1}\left[\begin{array}{c}41.63\\45.52\\72.87\end{array}\right] \\\\\\\left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{c}1.89\\5.75\\1.62\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%264%268%5C%5C6%262%2614%5C%5C8%263%2625%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D41.63%5C%5C45.52%5C%5C72.87%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%264%268%5C%5C6%262%2614%5C%5C8%263%2625%5Cend%7Barray%7D%5Cright%5D%20%5E%7B-1%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D41.63%5C%5C45.52%5C%5C72.87%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D1.89%5C%5C5.75%5C%5C1.62%5Cend%7Barray%7D%5Cright%5D)
The cost of chocolate pumpkins is $1.89, masks cost $5.75 and candy witches cost $1.62
Answer:
A = 78.5 cm^2
Step-by-step explanation:
The area of a circle is given by
A = pi r^2
We know r =5 and pi = 3.14
A = 3.14 (5^2)
A = 3.14 (25)
A = 78.5 cm^2
