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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?

Respuesta :

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:

[tex]\begin{gathered} A+B=149 \\ 5.70A+4.55B=790.65 \end{gathered}[/tex]

and solve the system:

[tex]\begin{gathered} A+B=149 \\ A+B-A=149-A \\ B=149-A \end{gathered}[/tex]

Substitute B in the second equation

[tex]\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 \\ \frac{1.15A}{1.15}=\frac{112.70}{1.15} \\ A=98 \end{gathered}[/tex]

Answer: Kaitlin used 98 pounds of type A coffee

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