Answer :
Final answer:
The worker used 36 pounds of nuts to make an 84-pound mixture, based on the given ratio of 1.5 pounds of nuts for every 2 pounds of fruit.
Explanation:
The question requires us to find out how many pounds of nuts are used by the worker to make an 84-pound mixture of nuts and dried fruit, given that the mixture has 1.5 pounds of nuts for every 2 pounds of fruit. Let's solve this with a ratio and proportion approach. The ratio of nuts to fruit is 1.5:2.
We can set up a proportion: 1.5 pounds of nuts / 2 pounds of fruit = x pounds of nuts / (84 - x) pounds of mixture (since x pounds are nuts, the rest of the mixture will be fruit).
Firstly, simplify the ratio to remove the decimal by multiplying both parts by 2, making it 3:4. So we have: 3 pounds of nuts / (3 + 4) pounds of mixture = x pounds of nuts / 84 pounds of mixture. This simplifies to: 3 / 7 = x / 84. Cross-multiplying gives: 3 * 84 = 7x. 252 = 7x. Dividing both sides by 7 gives: x = 36 pounds.
Therefore, the worker used 36 pounds of nuts to make the mixture.
