Question

Aldo’s coffee shop makes a blend that is a mixture of two types of coffee.Type A coffee costs 5.6 per pound. Type B costs 4.05 per pound. If 160 cups of blend are sold , for a total cost of 751.85. How many pounds of type B coffee did he use ?

Answer 1

Answer: 93

Step-by-step explanation:
`\\`Since 160 cups of blend are sold , this means

`\\`A + B = 160

`\\`Since Type A is sold for 5.6 per pound , that means the total number of A sold = 5.6A

`\\`Also , Type B is sold for 4.05 per pound , the total number of B sold = 4.05B

`\\`And it was given that the total cost of blend = 751.85 , then

5.6A + 4.05B = 751.85

`\\`A + B = 160 ............................. eqn 1

`\\`5.6A + 4.05B = 751.85 ..................... eqn II

`\\`From eqn I , A = 160 - B ................ eqn III

`\\`Substitute A = 160 - B into equation II , then we have:

`\\`5.6(160 - B) + 4.05B = 751.85

`\\`Expanding , we have

`\\`896 - 5.6B + 4.05B = 751.85

`\\`896 - 1.55B = 751.85

`\\`collecting the like terms

`\\`1.55B = 896 - 751.85

`\\`1.55B = 144.15

`\\`Therefore B = 144.15/1.55

`\\`B = 93