Bill is throwing a party. He wants to buy a pound and a half of mixed nuts. One third is almonds and two thirds are walnuts. The total cost is seven dollars and fifty cents. The almonds cost 4 dollars a pound. How much do the walnuts cost?
The correct answer and explanation is:
Here’s the solution and explanation for the cost of the walnuts.
Correct Answer:
The walnuts cost $5.50 per pound.
Explanation:
To determine the cost per pound of the walnuts, we need to break down the information provided about Bill’s purchase of mixed nuts. We know the total weight of the mix, the proportion of each type of nut, the total cost, and the cost per pound of the almonds. Our goal is to isolate the cost of the walnuts and then divide that by the weight of the walnuts to find their price per pound.
First, let’s calculate the exact weight of each type of nut in the 1.5-pound mix. The total weight is 1.5 pounds. We are told that one third (1/3) of this weight is almonds. To find the weight of almonds, we multiply the total weight by the almond proportion:
Weight of almonds = (1/3) * 1.5 pounds = 0.5 pounds.
Next, we find the weight of the walnuts. Walnuts make up two thirds (2/3) of the total weight.
Weight of walnuts = (2/3) * 1.5 pounds = 1.0 pound.
As a quick check, the weight of almonds (0.5 lbs) plus the weight of walnuts (1.0 lb) equals the total weight (1.5 lbs), confirming our calculations for the weights are correct.
Now that we know the weight of the almonds and their cost per pound, we can calculate how much the almonds contributed to the total cost of the mix. The almonds cost $4.00 per pound, and Bill bought 0.5 pounds of almonds.
Cost of almonds = Weight of almonds * Cost per pound of almonds
Cost of almonds = 0.5 pounds * $4.00/pound = $2.00.
The total cost of the entire 1.5 pounds of mixed nuts was $7.50. This total cost is the sum of the cost of the almonds and the cost of the walnuts. We know the total cost and the cost of the almonds, so we can find the cost of the walnuts by subtracting the cost of the almonds from the total cost:
Cost of walnuts = Total Cost – Cost of almonds
Cost of walnuts = $7.50 – $2.00 = $5.50.
So, the portion of the total bill that is attributable to the walnuts is $5.50.
Finally, we want to find the cost of the walnuts per pound. We know the total cost of the walnuts is $5.50 and the weight of the walnuts Bill bought was 1.0 pound. To find the cost per pound, we divide the total cost of the walnuts by their weight:
Cost per pound of walnuts = Cost of walnuts / Weight of walnuts
Cost per pound of walnuts = $5.50 / 1.0 pound = $5.50/pound.
Therefore, the walnuts cost $5.50 per pound.