Answer:
12.08 pounds of soy nuts and 14.08 pounds of trail mix
Explanation:
To determine the number of pounds of each item sold at the health food store, we need to first determine the total number of pounds of soy nuts and Asian trail mix sold. To do this, we can set up the following equation:
1.20p + 1.80q = 21.60
Here, p represents the number of pounds of soy nuts sold, and q represents the number of pounds of Asian trail mix sold. We know that the total sales for these items was $21.60, and that the price of soy nuts is $1.20 per pound and the price of Asian trail mix is $1.80 per pound. We also know that two more pounds of Asian trail mix were sold than soy nuts.
We can rearrange the equation to solve for p:
p = (21.60 - 1.80q) / 1.20
Since two more pounds of Asian trail mix were sold than soy nuts, we can set q equal to p + 2:
p = (21.60 - 1.80(p + 2)) / 1.20
We can then solve for p by dividing both sides by 1.20 and simplifying:
p = 14.50 / 1.20
This gives us a value of p = 12.08. Since the number of pounds of soy nuts sold is 12.08 and the number of pounds of Asian trail mix sold is two more than this, we can say that the number of pounds of Asian trail mix sold is 12.08 + 2 = 14.08.
Therefore, the health food store sold 12.08 pounds of soy nuts and 14.08 pounds of Asian trail mix.