Answer:
The bakery will bake 600 butterscotch bread, 550 chocolate bread, and 1,000 coconut bread
Step-by-step explanation:
In order to answer the word problem question, we list the parameters as follows;
The number of bread types the bakery takes = 3 types of bread
The monthly cost of the bakery for baking the bread, C = RM 6,850
The number of bread loaves baked = 2,150
The cost of baking a loaf of butterscotch bread = Rm 2
The cost of baking a loaf of chocolate bread = Rm 3
The cost of baking a loaf of coconut bread = Rm 4
The sale price of a butterscotch bread = Rm 3
The sale price of a chocolate bread = Rm 4.50
The sale price of a coconut bread = Rm 5
The amount of monthly profit the bakery makes, P = Rm 2,975
Therefore, the total revenue of the company, R = C + P
∴ R = Rm 6,850 + Rm 2,975 = Rm 9,825
Let 'x', 'y', and 'z', represent the number of loaves of butterscotch, chocolate, and coconut bread the company bakes respectively
Then we get;
x + y + z = 2,150...(1)
2·x + 3·y + 4·z = 6,850...(2)
3·x + 4.5·y + 5·z = 9,825...(3)
Multiplying equation (1) by 2 and subtracting from equation (2) gives;
2·x + 3·y + 4·z - 2×(x + y + z) = 6,850 - 2 × 2,150 = 2,550
2·x - 2·x + 3·y - 2·y + 4·z - 2·z = 2,550
∴ y + 2·z = 2,550...(4)
Adding equation (1) to (2) and subtracting from (3) gives;
3·x - 3·x + 4.5·y - 4·y + 5·z - 5·z = 9,825 - (6,850 + 2,150) = 825
1.5·y = 825
y = 825/1.5 = 550
The number of loaves of chocolate bread baked, y = 550
From equation (4), we get;
550 + 2·z = 2,550
2·z = 2,550 - 550 = 2,000
z = 2,000/2 = 1,000
The number of loaves of coconut bread baked, z = 1,000
∴ From equation (1) x = 2,150 - (550 + 1,000) = 600
The number of loaves of butterscotch bread baked, x = 600.
