Respuesta :
Answer:
8 pounds of raisin, 6 pounds of granola and 16 pounds of peanuts
Step-by-step explanation:
Lets form equations first.
->Peanuts cost $2.50 per pound, raisins cost $2.00 per pound, granola costs $4.00 per pound
2.50p + 2.00r + 4.00g= 80 -->eq(1)
-> bought ingredients to make 30 pounds of trail mix
p+ r+ g= 30 -->eq(2)
->If you use twice as many pounds of peanuts as raisins
2r=p
eq(1)=> 2.50p + 2.00r + 4.00g= 80
2.5(2r) + 2r +4g =80
5r + 2r + 4g =80
7r + 4g =80
eq(2)=>
2r+ r+ g= 30
3r + g =30
-4(3r + g =30)
7r + 4g =80
_______________
-5r = -40
r= 40/5 =>8
For 'g':
3(8) + g =30
g= 6
For 'p':
2r=p
p=16
therefore, 8 pounds of raisin, 6 pounds of granola and 16 pounds of peanuts should be bought
You need to buy 16 pounds of peanuts, 8 pounds of raisins, and 6 pounds of granola for each ingredient.
Given that,
You manage a health food store and budget $80 to buy ingredients to make 30 pounds of trail mix.
Peanuts cost $2.50 per pound, raisins cost $2.00 per pound, and granola costs $4.00 per pound.
We have to determine,
If you use twice as many pounds of peanuts as raisins, how many pounds of each ingredient should you buy?
According to the question,
Peanuts cost p= $2.50 per pound,
raisins cost r = $2.00 per pound,
and granola cost g = $4.00 per pound.
Sum of all the ingredients = budget to buy the ingredients,
[tex]\rm 2.50p + 2.00r + 4.00g= 80[/tex]
And ingredients required to make 30 pounds of trail mix,
[tex]p + r + g = 30[/tex]
If you use twice as many pounds of peanuts as raisins,
[tex]2r = p[/tex]
On solving the equation,
Substitute the value of p in equation 1 and equation 2,
[tex]\rm 2.50(2r) + 2.00r + 4.00g= 80\\\\5r + 2r + 4g = 800\\\\7r + 4g = 800[/tex]
Then,
[tex]2r + r + g = 30\\\\3r + g = 30\\\\ g = 30-3r[/tex]
Substitute value of g in the equation,
[tex]7r + 4g = 80\\\\7r + 4(30-3r) = 80\\\\7r + 120 - 12r = 800\\\\-5r = 80 - 120\\\\ -5r = -40\\\\ r = \dfrac{-40}{-5}\\\\ r = 8[/tex]
Then the value of p,
[tex]2r = p\\\\p = 2(8) \\\\p = 16[/tex]
And the value of g is,
[tex]p + r +g = 30\\\\8 + 16 + g = 30\\\\24 + g = 30\\\\g = 30-24\\\\g = 6[/tex]
Hence, You need to buy 16 pounds of peanuts, 8 pounds of raisins, and 6 pounds of granola for each ingredient.
For more details refer to the link.
https://brainly.com/question/18275965
