Answer:
5 pounds of Cereal A
2 pounds of Cereal B
3 pounds of Cereal C
Step-by-step explanation:
Let x represent grams of cereal A
Let y represent grams of cereal B
Let z represent grams of cereal C
For potassium needed,
10g of cereal A, 6g of cereal B and 12g of cereal C which totals to 98g
Mathematically, we have 10x + 6y + 12z = 98 --------- Equation 1
For calcium,
2g of cereal A, 0g of cereal B and 6g of cereal C which totals to 28g.
Mathematically, we have 2x + 0y + 6z = 28
2x + 6z = 28 ---------- Equation 2
For magnesium
4g of cereal A, 3g of cereal B and 2g of cereal C, which totals to 32g
Mathematically, we have 4x + 3y + 2z = 32 ----------- Equation 3
Write out the three equations
10x + 6y + 12z = 98
2x + 6z = 28
4x + 3y + 2z = 32
We solve the above simultaneous equations using substitution method
In equation 2, we make x the subject of the formula
From 2x + 6z = 28
We have; 2x = 28 - 6z --------- Divide through by 2
2x/2 = (28-6z)/2
x = 28/2 - 6z/2
x = 14 - 3z ------------ Equation 4
Substitute (14-3z) for x in equation 1 and 2
In equation 1,
From 10x + 6y + 12z = 98
We have 10(14-3z) + 6y + 12z = 98 ---------- Open the bracket
140 - 30z + 6y + 12z = 98 -------------- Collect like terms
6y + 12z - 30z= 98 - 140
6y - 18z = -42 --------------- Divide through by 6
(6y - 18z)/6 = -42/6
y - 3z = -7 ---------------- Make y the subject of formula
y = 3z - 7 ------------- Equation 5
In equation 3,
From 4x + 3y + 2z = 32
We have; 4(14-3z) + 3y+ 2z = 32 -------------- Open the bracket
56 - 12z + 3y + 2z = 32 ------------------- Collect like terms
3y + 2z - 12z = 32 - 56
3y - 10z = -24 ---------------- Equation 6
Substitute (3z - 7) for y in equation 6
In equation 6;
From 3y - 10z = -24
We have 3(3z - 7) - 10z= -24 ------------ Open the bracket
9z - 21 - 10z = -24 ------- Collect like terms
9z- 10z = -24 +21
-z = -3
z = 3
Substitute 3 for z in equation 5
In equation 5;
From y = 3z - 7
We have; y = 3(3) - 7
y = 9 - 7
y = 2
Substitute 3 for z in equation 4
In equation 4;
From x= 14- 3z
We have; x = 14 - 3(3)
x = 14 - 9
x = 5
So, x = 5 y = 2 and z= 3