If the total value of the coins is $15. The number of each type of coin is: 31 quarters, 72 dimes.
<h3>Number of each type of coin</h3>
Let D = number of dimes
Let Q = the number of quarters
Equations
d + q = 103
0.10d + 0.25q = 15
d = 103 -q
0.10(103 -q) + 0.25q = 15
10.3 - 0.10q + 0.25q = 15
0.15q = 4.7
q=4.7/0.15
q=31 quarters
Substitute q into second equation
D+31=103
D=72 dimes
Therefore the number of each type of coin is: 31 quarters, 72 dimes.
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The solution to the system of equations x + 2y = 1 and -3x-2y = 5 is:
x = -3, y = 2
The given system of equations:
x + 2y = 1............(1)
-3x - 2y = 5..........(2)
This can be written in matrix form as shown:
![\left[\begin{array}{ccc}1&2\\-3&-2\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}1\\5\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%262%5C%5C-3%26-2%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%5C%5C5%5Cend%7Barray%7D%5Cright%5D)
Find the determinant of ![\left[\begin{array}{ccc}1&2\\-3&-2\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%262%5C%5C-3%26-2%5Cend%7Barray%7D%5Cright%5D)
![\triangle_x = \left[\begin{array}{ccc}1&2\\5&-2\end{array}\right]\\\triangle_x = 1(-2)-2(5)\\\triangle_x = -2-10\\\triangle_x =-12](https://tex.z-dn.net/?f=%5Ctriangle_x%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%262%5C%5C5%26-2%5Cend%7Barray%7D%5Cright%5D%5C%5C%5Ctriangle_x%20%3D%201%28-2%29-2%285%29%5C%5C%5Ctriangle_x%20%3D%20-2-10%5C%5C%5Ctriangle_x%20%3D-12)
![\triangle_y = \left[\begin{array}{ccc}1&1\\-3&5\end{array}\right]\\\triangle_y = 1(5)-1(-3)\\\triangle_y = 5 + 3\\\triangle_y =8](https://tex.z-dn.net/?f=%5Ctriangle_y%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%261%5C%5C-3%265%5Cend%7Barray%7D%5Cright%5D%5C%5C%5Ctriangle_y%20%3D%201%285%29-1%28-3%29%5C%5C%5Ctriangle_y%20%3D%205%20%2B%203%5C%5C%5Ctriangle_y%20%3D8)
The solution to the system of equations x + 2y = 1 and -3x-2y = 5 is:
x = -3, y = 2
Learn more here: brainly.com/question/4428059
Answer:
18
Step-by-step explanation:
Answer:
. B. For every 8 french fries, there is 1 packet of ketchup
Step-by-step explanation:
THIS ARE THE OPTIONS FOR THE QUESTION
A. There are 7 more french fries than packets of ketchup. B. For every 8 french fries, there is 1 packet of ketchup. C. For every 8 packets of ketchup, there is 1 french fry. D. There are 8 more french fries than packets of ketchup.
Ratio expresses quotient of two mathematical expressions. It gives relationship in term of quantity, amount existing between two or more things. From the question, it shows that when ever there is 8 french fries, there would be 1 packet of ketchup. I.e french fries and ketchup are in ratio of 8:1
