Answer:
Let the type A coffee be
[tex]=x[/tex]Let the type B coffee be
[tex]=y[/tex]Three times as many pounds of type B coffee as type A, will be represented below as
[tex]y=3x[/tex]The cost of type A coffee is
[tex]=\text{ \$4.10 per pound}[/tex]The cost of type B is
[tex]=\text{ \$5.25 per pound}[/tex]The total cost of both coffee is
[tex]=\text{ \$635.20}[/tex]Hence,
The equation will be
[tex]\begin{gathered} 4.10x+5.25y=635.20 \\ 4.10x+5.25(3x)=635.20 \\ 4.10x+15.75x=635.20 \\ 19.85x=635.20 \\ \frac{19.85x}{19.85}=\frac{635.20}{19.85} \\ x=32 \end{gathered}[/tex]Hence,
The number of pounds of type A coffee is = 32 pounds
