Question

How much of each do they need to use? I need all of whata in the photo to be complete

Answer 1

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

`21*29\text{ \%=21}*(29)/(100)=6.09`
`a*35\text{ \%=a}*(35)/(100)=0.35a`
`b*25\text{ \%=b}*(25)/(100)=0.25b`

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

`a+b=21\rightarrow(1)`
`0.35a+0.25b=6.09\rightarrow(2)`

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

`\begin{gathered} (-0.25)(a)+(-0.25)(b)=(-0.25)(21) \\ -0.25a-0.25b=-5.25\rightarrow(3) \end{gathered}`

Add equations (2) and (3) to eliminate b

`\begin{gathered} (0.35a-0.25a)+(0.25b-0.25b)=(6.09-5.25) \\ 0.10a=0.84 \end{gathered}`

Divide each side by 0.10

`\begin{gathered} (0.10a)/(0.10)=(0.84)/(0.10) \\ a=8.4 \end{gathered}`

Substitute a in equation (1) by 8.4

`8.4+b=21`

Subtract 8.4 from each side

`\begin{gathered} 8.4-8.4+b=21-8.4 \\ b=12.6 \end{gathered}`

The amount of brand A nuts used is 8.4 oz

The amount of brand B nuts used is 12.6 oz