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 ?

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bayosanuade bayosanuade · Answer 1 · 2019-11-09T18:45:21+01:00

Answer: 93

Step-by-step explanation: [tex]\\[/tex]Since 160 cups of blend are sold , this means

[tex]\\[/tex]A + B = 160

[tex]\\[/tex]Since Type A is sold for 5.6 per pound , that means the total number of A sold = 5.6A

[tex]\\[/tex]Also , Type B is sold for 4.05 per pound , the total number of B sold = 4.05B

[tex]\\[/tex]And it was given that the total cost of blend = 751.85 , then

5.6A + 4.05B = 751.85

[tex]\\[/tex]A + B = 160 ............................. eqn 1

[tex]\\[/tex]5.6A + 4.05B = 751.85 ..................... eqn II

[tex]\\[/tex]From eqn I , A = 160 - B ................ eqn III

[tex]\\[/tex]Substitute A = 160 - B into equation II , then we have:

[tex]\\[/tex]5.6(160 - B) + 4.05B = 751.85

[tex]\\[/tex]Expanding , we have

[tex]\\[/tex]896 - 5.6B + 4.05B = 751.85

[tex]\\[/tex]896 - 1.55B = 751.85

[tex]\\[/tex]collecting the like terms

[tex]\\[/tex]1.55B = 896 - 751.85

[tex]\\[/tex]1.55B = 144.15

[tex]\\[/tex]Therefore B = 144.15/1.55

[tex]\\[/tex]B = 93