Question

Mai's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Mai $5.80 per pound, and type B coffee costs $4.75 per pound. This month, Mai made 153 pounds of the blend, for a total cost of $796.05. How many pounds of type B coffee did she use

Answer 1

We can solve this problem using a method called substitution.

We will use two variables-x for the Type A and y for the Type B.

We already know that a total of 153 pounds was used. We will represent this using the equation x+y=153.

We also know that the Type A costs 5.80/pound, and the Type B costs 4.75. The total cost is 796.05.

We will use the equation 5.8x+4.75y=796.05.

We now have our two equations:

x+y=153

5.8x+4.75y=796.05

Next, we will use the first equation to isolate one of the variables. Let's isolate x.

We will isolate x by subtracting y from both sides of the equation.

We now have:

x=153-y

We will now plug this in for x in the second equation.

5.8(153-y)+4.75y=796.05

We get rid of the parentheses using the Distributive Property.

887.4-5.8y+4.75y=796.05

887.4-1.05y=796.05

-1.05y=-91.35

y=87

We now use this to solve for x.

5.8x+4.75y=796.05

5.8x+413.25=796.05

5.8x=382.8

x=66

Type A=66

Type B=87

Hope this helped!