Question

Rueben's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Rueben $4.40 per pound, and type B coffee costs $5.70 per pound. This month, Rueben made 165 pounds of the blend, for a total cost of $841.70 . How many pounds of type B coffee did he use?

Answer 1

165=x+y
841.70=4.4x+5.7y

Answer 2

you can see this by making pounds of type A = x and pounds of type B = y

you know he bought 165 pounds therefore you know that x and y have to equal 165

165=x+y

now you know it costed 841.70 all together and you know that type a costs 4.4 per pound(x) and type b costs 5.7 per pound (y)... replacing these into a equation you get

841.7=4.4x+5.7y

Answer 3

so how do you get the answer

Answer 4

now use substitution by solving the top equation for y

165=x+y

165-x=x-x+y [subtract both sides by x]

165-x=y

take this equation and substitute it into the second

841.70=4.4x+5.7(165-x)

841.70=4.4x+940.5-5.7x [distributed 5.7 to (165-x)]

841.70-940.5=4.4x+940.5-940.5-5.7x [ subtracted 940.5 from both sides]

-98.8=-1.3x [added like terms]

-98.8/-1.3=-1.3x/-1.3 [divided by -1.3 on both sides]

76 = x

now you know that he bought 76 pounds of Type A

to find Type B go back to your first equation

165=x+y

since x=76

165=76+y

165-76=76-76+y [substract 76 from both sides]

89= y

89 bounds of type B

Answer 5

Let x =amount of Type A
then 165-x= amount of Type B
4.40x +5.70(165-x)=841.70

Answer 6

Solve that equation.