Answer:
The store mixes 8 pounds of peanuts and 9 pounds of raisins.
Step-by-step explanation:
Let the store mixes 'x' pounds of peanuts and 'y' pounds of raisins.
The cost of peanut per pound is $3.20 and cost of raisins per pound $2.10
According to question,
Total weight of mixture given is 17 pounds.
[tex]\Rightarrow x+y=17[/tex] ................(1)
also total cost of mixture given is $44.50
[tex]\Rightarrow 3.20x+2.10y=44.50[/tex] ...........(2)
Solving for equation (1) and (2),
Multiply equation (1) by 3.20 , we get
(1)⇒ [tex]3.20x+3.20y=54.40[/tex] ............(3)
Now, subtract equation (3) from equation (2) , we get
[tex]3.20x+2.10y-(3.20x+3.20y)=44.50-54.40[/tex]
[tex]\Rightarrow 3.20x+2.10y-3.20x-3.20y=-9.90[/tex]
[tex]\Rightarrow 2.10y-3.20y=-9.90[/tex]
[tex]\Rightarrow -1.1y=-9.90[/tex]
[tex]\Rightarrow y=9[/tex]
Thus, The store mixes 9 pounds of raisins.
Put, y = 9 in (1),
[tex]\Rightarrow x+y=17 \Rightarrow x+9=17 \Rightarrow x=8[/tex]
Thus, The store mixes 8 pounds of peanuts.
