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Sagot :
Let x be the number of pounds of the $2.00 candy and let y be the number of pounds of the $2.85 candy.
We know that in total the grocer wants 21 pounds, this can be express by the equation:
[tex]x+y=21[/tex]We also know that the grocer wants the mix to cost $2.05 per pound. This condition can be express as:
[tex]\begin{gathered} 2x+2.85y=2.05\cdot21 \\ 2x+\text{2}.85y=43.05 \end{gathered}[/tex]Hence we have the system of equations:
[tex]\begin{gathered} x+y=21 \\ 2x+2.85y=43.05 \end{gathered}[/tex]To solve ithe system we solve the first equation for y:
[tex]y=21-x[/tex]and we plug this value in the second equation:
[tex]\begin{gathered} 2x+2.85(21-x)=43.05 \\ 2x+59.85-2.85x=43.05 \\ -0.85=43.05-59.85 \\ -0.85x=-16.8 \\ x=\frac{-16.8}{-0.85} \\ x=19.76 \end{gathered}[/tex]Now we plug the value of x in the expression for y we found earlier:
[tex]\begin{gathered} y=21-19.76 \\ y=\text{1}.24 \end{gathered}[/tex]Therefore, the grocer needs 19.76 pounds of the $2.00 candy and 1.24 pounds of the $2.05 candy
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