Question

Kaitlin's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Kaitlin $5.70 per pound, and type B coffee costs $4.55 perpound. This month, Kaitlin made 149 pounds of the blend, for a total cost of $790.65. How many pounds of type A coffee did she use?

Answer 1

We have:

Type A coffee $5.70 per pound

Type B coffee $4.55 per pound

Total cost $790.65

Total blend 149 pounds

Then we have the following equations:

`\begin{gathered} A+B=149 \\ 5.70A+4.55B=790.65 \end{gathered}`

and solve the system:

`\begin{gathered} A+B=149 \\ A+B-A=149-A \\ B=149-A \end{gathered}`

Substitute B in the second equation

`\begin{gathered} 5.70A+4.55(149-A)=790.65 \\ 5.70A+677.95-4.55A=790.65 \\ 1.15A+677.95=790.65 \\ 1.15A+677.95-677.95=790.65-677.95 \\ 1.15A=112.70 \\ (1.15A)/(1.15)=(112.70)/(1.15) \\ A=98 \end{gathered}`

Answer: Kaitlin used 98 pounds of type A coffee