Since a represents the amount of brand A used
Since b represents the amount of brand B used
Since Total weight x Percent peanuts = Weight of peanuts
[tex]21\times29\text{ \%=21}\times\frac{29}{100}=6.09[/tex][tex]a\times35\text{ \%=a}\times\frac{35}{100}=0.35a[/tex][tex]b\times25\text{ \%=b}\times\frac{25}{100}=0.25b[/tex]Let us complete the table
Brand A mixed nuts: a 0.35 0.35a
Brand B mixed nuts: b 0.25 0.25b
Planter mixed nuts: 21 0.29 6.09
Let us write the 2 equation
[tex]a+b=21\rightarrow(1)[/tex][tex]0.35a+0.25b=6.09\rightarrow(2)[/tex]Now we need to solve them algebraically
Multiply equation (1) by -0.25 to make the coefficients of b equal in values and different in signs
[tex]\begin{gathered} (-0.25)(a)+(-0.25)(b)=(-0.25)(21) \\ -0.25a-0.25b=-5.25\rightarrow(3) \end{gathered}[/tex]Add equations (2) and (3) to eliminate b
[tex]\begin{gathered} (0.35a-0.25a)+(0.25b-0.25b)=(6.09-5.25) \\ 0.10a=0.84 \end{gathered}[/tex]Divide each side by 0.10
[tex]\begin{gathered} \frac{0.10a}{0.10}=\frac{0.84}{0.10} \\ a=8.4 \end{gathered}[/tex]Substitute a in equation (1) by 8.4
[tex]8.4+b=21[/tex]Subtract 8.4 from each side
[tex]\begin{gathered} 8.4-8.4+b=21-8.4 \\ b=12.6 \end{gathered}[/tex]The amount of brand A nuts used is 8.4 oz
The amount of brand B nuts used is 12.6 oz