A shop owner blends three types of coffee,A,B,C.in the ratio 3:5:7
a) calculate the weight of each type of coffee in 45kg of three blended mixture.
b) given that type A coffee cost $7 per kg, type B coffee costs $10 kg and type C coffee costs $13 per kg, calculate the cost per kg of the blended mixture
3x + 5x + 7x = 45
15x = 45
x = 3
A = 9 B= 15 C = 21
9(7) + 15(10) + 21(13)=486
486/45 = cost/kg
10.8 cost/kg for the mix.
3x+5x+7x=45
15x=45
x=3
A=9 B=15 C=21
9(7)+15(10)+21(13)=486
486/45 =cost/kg
10.80 cost/kg for mixture
Sol:
Wt. of each type of coffee
= 3+5+7
= 15
= 3x3 3x5 3x7
= 9kg,15kg,21kg
3*3
a) Sure, let's calculate the weights of each type of coffee in a 45kg blended mixture.
The ratio of type A to type B to type C coffee is 3:5:7. This means we need to calculate the weights of each type of coffee using this ratio.
To calculate the weight of type A coffee:
Weight of Type A coffee = (3 / (3 + 5 + 7)) * 45 kg
Weight of Type A coffee = (3 / 15) * 45 kg
Weight of Type A coffee = 9 kg
To calculate the weight of type B coffee:
Weight of Type B coffee = (5 / (3 + 5 + 7)) * 45 kg
Weight of Type B coffee = (5 / 15) * 45 kg
Weight of Type B coffee = 15 kg
To calculate the weight of type C coffee:
Weight of Type C coffee = (7 / (3 + 5 + 7)) * 45 kg
Weight of Type C coffee = (7 / 15) * 45 kg
Weight of Type C coffee = 21 kg
So in a 45kg blended mixture, there would be 9kg of type A coffee, 15kg of type B coffee, and 21kg of type C coffee.
b) Now let's calculate the cost per kg of the blended mixture using the given prices.
Cost per kg of the blended mixture = ((Cost per kg of Type A coffee * Weight of Type A coffee) + (Cost per kg of Type B coffee * Weight of Type B coffee) + (Cost per kg of Type C coffee * Weight of Type C coffee)) / Total weight of the blended mixture
Cost per kg of the blended mixture = (($7/kg * 9 kg) + ($10/kg * 15 kg) + ($13/kg * 21 kg)) / 45 kg
Cost per kg of the blended mixture = ($63 + $150 + $273) / 45 kg
Cost per kg of the blended mixture = $486 / 45 kg
Cost per kg of the blended mixture ≈ $10.80/kg
So, the cost per kg of the blended mixture would be approximately $10.80/kg.
To solve this problem, we will first determine the weight of each type of coffee in the blended mixture and then calculate the cost per kilogram of the blended mixture.
a) Calculate the weight of each type of coffee in 45kg of the blended mixture.
1. Start by determining the total number of parts in the ratio (3 + 5 + 7 = 15). The total number of parts represents the total number of equal parts we have for the three types of coffee.
2. To find the weight of each type of coffee, we need to divide the total weight of the blend (45kg) by the total number of parts (15kg).
Weight of type A coffee = (3/15) * 45kg = 9kg
Weight of type B coffee = (5/15) * 45kg = 15kg
Weight of type C coffee = (7/15) * 45kg = 21kg
Therefore, in a 45kg blended mixture, the weight of type A coffee is 9kg, the weight of type B coffee is 15kg, and the weight of type C coffee is 21kg.
b) Calculate the cost per kilogram of the blended mixture.
To calculate the cost per kilogram of the blended mixture, we need to multiply the weight of each type of coffee by its respective cost per kilogram, sum them up, and then divide that total by the total weight of the blend.
Cost per kg of type A coffee = $7
Cost per kg of type B coffee = $10
Cost per kg of type C coffee = $13
Total cost = (Cost per kg of type A coffee * Weight of type A coffee) +
(Cost per kg of type B coffee * Weight of type B coffee) +
(Cost per kg of type C coffee * Weight of type C coffee)
Total cost = ($7 * 9kg) + ($10 * 15kg) + ($13 * 21kg)
Total cost = $63 + $150 + $273
Total cost = $486
Cost per kg of the blended mixture = Total cost / Total weight of the blend
Cost per kg of the blended mixture = $486 / 45kg
Cost per kg of the blended mixture = $10.80 (rounded to two decimal places)
Therefore, the cost per kilogram of the blended mixture is $10.80.