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Sagot :
let us begin by assigning letters to the variables here. Hence, let the City Roast Colombian be x, while the French Roast Columbian be y. If the mixture of 1 pound of City roast and 1 pound of French roast would cost $7.83 per pound (for the mixture), then we can have the expression developed into an equation as follows;
[tex]7.80x+8.10y=7.83(20)[/tex]Also, to make a 20 pound blend would simply mean;
[tex]x+y=20[/tex]We now have a system of equations which we can solve as follows;
[tex]\begin{gathered} 7.80x+8.10y=156.60---(1) \\ x+y=20---(2) \\ \text{From equation (2), make x the subject and we'll have;} \\ x=20-y \\ \text{Substitute for the value of x into equation (1)} \\ 7.80(20-y)+8.10y=156.60 \\ 156-7.80y+8.10y=156.60 \\ \text{Collect all like terms;} \\ 8.10y-7.80y=156.60-156 \\ 0.3y=0.60 \\ \text{Divide both sides by 0.3} \\ \frac{0.3y}{0.3}=\frac{0.6}{0.3} \\ y=2 \end{gathered}[/tex]We can now substitute for the value of y into equation (2), as follows;
[tex]\begin{gathered} x+y=20 \\ x+2=20 \\ \text{Subtract 2 from both sides;} \\ x+2-2=20-2 \\ x=18 \end{gathered}[/tex]Hence, we have;
[tex]x=18,y=2[/tex]ANSWER:
Julia and her husband should buy the coffee as follows;
[tex]\begin{gathered} \text{City Roast Columbian Coffee}=18\text{ pounds} \\ \text{French Roast Columbian Coffee}=2\text{ pounds} \end{gathered}[/tex]
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