Answer:
- Mix A is 2 units
- Mix B is 1 unit
- Mix C is 3 units
Step-by-step explanation:
Let amount of Mix A is a, Mix B is b, Mix C is c.
<u>With the given details, we get the following system</u>
- 5a + 6b + 4c = 28
- 4a + 2b + c = 13
- 3a + 4b + 4c = 22
Find the value of c (the easiest one) for substitution
Substitute c into the first equation
- 5a + 6b + 4(13 - 4a - 2b) = 28
- 5a + 6b + 52 - 16a - 8b = 28
- - 11a - 2b = 28 - 52
- 11a + 2b = 24 (5)
Substitute c into the third equation
- 3a + 4b + 4(13 - 4a - 2b) = 22
- 3a + 4b + 52 - 16a - 8b = 22
- - 13a - 4b = 22 - 52
- 13a + 4b = 30 (6)
Double the equation (5) and subtract (6), find the value of a
- 2(11a + 2b) - 13a - 4b = 2(24) - 30
- 22a - 13a = 48 - 30
- 9a = 18
- a = 2
Find b
- 11*2 + 2b = 24
- 22 + 2b = 24
- 2b = 2
- b = 1
Now find c
- c = 13 - 4*2 - 2*1
- c = 13 - 8 - 2
- c = 3
