Answer:
Coffee = $2.00
Juice = $1.50
Doughnut = $1.00
Step-by-step explanation:
Given
Let:
![c = coffee\\ j= juice\\ d = doughnut](https://tex.z-dn.net/?f=c%20%3D%20coffee%5C%5C%20j%3D%20juice%5C%5C%20d%20%3D%20doughnut)
So, we have:
Anna
![2c + j + 2d = 7.50](https://tex.z-dn.net/?f=2c%20%2B%20j%20%2B%202d%20%3D%207.50)
Barry
![c + 3d = 5.00](https://tex.z-dn.net/?f=c%20%2B%203d%20%3D%205.00)
Cathy
![3c + j + 4d = 11.50](https://tex.z-dn.net/?f=3c%20%2B%20j%20%2B%204d%20%3D%2011.50)
Required
The price of each
We have:
![2c + j + 2d = 7.50](https://tex.z-dn.net/?f=2c%20%2B%20j%20%2B%202d%20%3D%207.50)
![c + 3d = 5.00](https://tex.z-dn.net/?f=c%20%2B%203d%20%3D%205.00)
![3c + j + 4d = 11.50](https://tex.z-dn.net/?f=3c%20%2B%20j%20%2B%204d%20%3D%2011.50)
Make c the subject in: ![c + 3d = 5.00](https://tex.z-dn.net/?f=c%20%2B%203d%20%3D%205.00)
![c = 5.00 - 3d](https://tex.z-dn.net/?f=c%20%3D%205.00%20-%203d)
Substitute
in
and ![3c + j + 4d = 11.50](https://tex.z-dn.net/?f=3c%20%2B%20j%20%2B%204d%20%3D%2011.50)
![2c + j + 2d = 7.50](https://tex.z-dn.net/?f=2c%20%2B%20j%20%2B%202d%20%3D%207.50)
![2[5.00 - 3d] + j + 2d = 7.50](https://tex.z-dn.net/?f=2%5B5.00%20-%203d%5D%20%2B%20j%20%2B%202d%20%3D%207.50)
![10.00 - 6d+ j + 2d = 7.50](https://tex.z-dn.net/?f=10.00%20-%206d%2B%20j%20%2B%202d%20%3D%207.50)
Make j the subject
![j = 7.50 - 10.0 +6d - 2d](https://tex.z-dn.net/?f=j%20%3D%207.50%20-%2010.0%20%2B6d%20-%202d)
![j = -2.50 +4d](https://tex.z-dn.net/?f=j%20%3D%20-2.50%20%2B4d)
![3c + j + 4d = 11.50](https://tex.z-dn.net/?f=3c%20%2B%20j%20%2B%204d%20%3D%2011.50)
![3[5.00 - 3d] + j + 4d = 11.50](https://tex.z-dn.net/?f=3%5B5.00%20-%203d%5D%20%2B%20j%20%2B%204d%20%3D%2011.50)
![15.00 - 9d + j + 4d = 11.50](https://tex.z-dn.net/?f=15.00%20-%209d%20%2B%20j%20%2B%204d%20%3D%2011.50)
Make j the subject
![j = 11.50 - 15.00 + 9d -4d](https://tex.z-dn.net/?f=j%20%3D%2011.50%20-%2015.00%20%2B%209d%20-4d)
![j = -3.50 + 5d](https://tex.z-dn.net/?f=j%20%3D%20-3.50%20%2B%205d)
So, we have:
and ![j = -2.50 +4d](https://tex.z-dn.net/?f=j%20%3D%20-2.50%20%2B4d)
Equate both values of j
![-3.50 + 5d = -2.50 + 4d](https://tex.z-dn.net/?f=-3.50%20%2B%205d%20%3D%20-2.50%20%2B%204d)
Collect like terms
![5d - 4d = 3.50 -2.50](https://tex.z-dn.net/?f=5d%20-%204d%20%3D%203.50%20-2.50)
![d = 1.00](https://tex.z-dn.net/?f=d%20%3D%201.00)
Substitute
in ![j = -3.50 + 5d](https://tex.z-dn.net/?f=j%20%3D%20-3.50%20%2B%205d)
![j = -3.50 + 5d](https://tex.z-dn.net/?f=j%20%3D%20-3.50%20%2B%205d)
![j = -3.50 + 5 * 1.00](https://tex.z-dn.net/?f=j%20%3D%20-3.50%20%2B%205%20%2A%201.00)
![j = -3.50 + 5.00](https://tex.z-dn.net/?f=j%20%3D%20-3.50%20%2B%205.00)
![j = 1.50](https://tex.z-dn.net/?f=j%20%3D%201.50)
To solve for c, we substitute
in ![c + 3d = 5.00](https://tex.z-dn.net/?f=c%20%2B%203d%20%3D%205.00)
![c + 3 * 1.00 =5.00](https://tex.z-dn.net/?f=c%20%2B%203%20%2A%201.00%20%3D5.00)
![c + 3.00 =5.00](https://tex.z-dn.net/?f=c%20%2B%203.00%20%3D5.00)
Solve for c
![c =- 3.00 +5.00](https://tex.z-dn.net/?f=c%20%3D-%203.00%20%2B5.00)
![c =2.00](https://tex.z-dn.net/?f=c%20%3D2.00)
Equivalent fractions are fractions that have the same value. They can be found by reducing the fraction or by multiplying both the numerator and denominator by the same number.
In this case, 4 and 12 can both be divided by 4, so the fraction 4/12 can be reduced to 1/3.
Answer: 1.5(b)+ 2.25(s) = 10.05
Step-by-step explanation:
<span>The differential equation:
dy/dt = a*y + b = a*(y + b/a) </span>
292in^3
3x6x10=180 because I’ve split the shape in half
7x4x4=112
180+112=292