Respuesta :
Answer:
3 ounces of apricots, 6 ounces of peanuts and 7 ounces of raisins.
Step-by-step explanation:
Given:
One pound of the mixture costs $3.18.
It contains twice as much peanuts by weight as apricots.
One pound of dried apricots costs $4.48
One pound of raisins cost $2.40.
One pound of peanuts cost $3.44.
Question asked:
How many ounces of each ingredient are contained in 1 pound of the trail mix ?:
Solution:
Let one pound mixture contains apricots = [tex]x\ pound[/tex]
So, one pound mixture contains peanuts = [tex]2x\ pound[/tex]
So, one pound mixture contains raisins = [tex]1-(x+2x)=1-3x\ pound[/tex]
To calculate cost of one pound mixture, we will multiply the amount of each ingredients present in one pound mixture with their respective costs:
One pound of dried apricots costs = $4.48
[tex]x\ pound[/tex] of dried apricots costs = [tex]4.48x[/tex]
One pound of peanuts cost = $3.44.
[tex]2x\ pound[/tex] of peanuts cost = [tex]3.44\times2x=6.88x[/tex]
One pound of raisins cost = $2.40.
[tex]1-3x\ pound[/tex] of raisins cost = [tex](1-3x)\times2.40=2.40-7.2 x[/tex]
Now, as given one pound of mixture cost = $3.18.
[tex]4.48x+6.88x+(2.40-7.2x)=3.18\\11.36x+2.40-7.2x=3.18\\4.16x+2.40=3.18[/tex]
Subtracting both sides by 2.40
[tex]4.16x=0.78\\[/tex]
Dividing both sides by 4.16
[tex]x=0.1875=\frac{3}{16}[/tex]
One pound mixture contains apricots = [tex]x\ pound[/tex] = [tex]\frac{3}{16} \ pound[/tex]
Now, convert it into ounces;
1 pound = 16 ounces
[tex]\frac{3}{16} \ pound[/tex] = [tex]16\times\frac{3}{16} =3\ ounces[/tex]
One pound mixture contains peanuts = [tex]2x\ pound=2\times\frac{3}{16} =\frac{6}{16} \ pound[/tex]
[tex]\frac{6}{16} \ pounds = \frac{6}{16}\times16=6\ ounces[/tex]
one pound mixture contains raisins = [tex]1-3x=1-(3\times\frac{3}{16}) =1-\frac{9}{16} =\frac{16\times1-1\times9}{16} =\frac{7}{16}\ pound[/tex]
[tex]\frac{7}{16} \ pound=\frac{7}{16}\times16=7\ ounces[/tex]
Therefore, 1 pound of the trail mix contains 3 ounces of apricots, 6 ounces of peanuts and 7 ounces of raisins.
