Did not ask offers a mixture of Celine it’s an almond almond sale for seven dollars per pound in Salinas sell for $5.50 per pound the net house will May 20 pounds of the mixed nuts and sell mixture for $5.95 per pound. The following equations represent the problem with keeping the cost of mixture, consistent with the ingredients how many pounds of swing that should be used in the mixture.
Let's assume the number of pounds of almonds in the mixture is x.
According to the given information, the cost per pound of Celine almonds is $7.
So, the total cost of Celine almonds in the mixture is 7x dollars.
The cost per pound of almonds in Salinas is $5.50.
Thus, the total cost of almond nuts in Salinas in the mixture is 5.5(20 - x) dollars. (Note that we subtract x from 20 to represent the remaining pounds of almonds in Salinas in the mixture)
The net cost of the mixture is given as $5.95 per pound.
Therefore, the total cost of the mixture is 5.95 * 20 dollars.
According to the problem, the cost of the mixture needs to be consistent with the ingredients. Thus, we can set up the following equation:
7x + 5.5(20 - x) = 5.95 * 20
Now, we can solve the equation to find the value of x, which represents the number of pounds of almonds needed in the mixture.
To solve this problem, let's denote the number of pounds of almonds needed as x.
Since the cost of almonds is $7 per pound, the cost of the almonds used in the mixture would be 7x.
Similarly, let's denote the number of pounds of cashews needed as y.
Since the cost of cashews is $5.50 per pound, the cost of cashews used in the mixture would be 5.50y.
According to the given information, the net house will make 20 pounds of the mixed nuts.
So, the total weight of the mixture is 20 pounds, which can be written as: x + y = 20.
Now, let's determine the cost of the mixture.
The mixture is sold for $5.95 per pound, so the total cost of the mixture would be 5.95 multiplied by 20 (the total weight).
The cost of the mixture can also be written as 7x + 5.50y.
Since the cost of the mixture should be consistent with the ingredients, we can set up the following equation:
7x + 5.50y = 5.95 × 20
Now we have a system of equations:
x + y = 20
7x + 5.50y = 5.95 × 20
By solving this system of equations, we can find the values of x and y, which represent the pounds of almonds and cashews needed in the mixture.
To solve this problem, you need to set up a system of equations based on the information provided. Let's define the variables:
Let x represent the pounds of Celine almonds used in the mixture.
Let y represent the pounds of Salinas almonds used in the mixture.
Now, let's set up the equations based on the information given:
Equation 1: The cost of the Celine almonds at $7 per pound plus the cost of the Salinas almonds at $5.50 per pound should be consistent with the cost of the mixture at $5.95 per pound. This can be represented as:
(7x + 5.50y) / (x + y) = 5.95
Equation 2: The total weight of the mixture is given as 20 pounds:
x + y = 20
Now we have a system of two equations with two variables. We can solve this system to find the values of x and y, which represent the pounds of Celine and Salinas almonds, respectively, needed in the mixture.
To solve the system, we can use various methods such as substitution or elimination. Let's use the substitution method here.
1. Solve Equation 2 for x:
x = 20 - y
2. Substitute the value of x in Equation 1:
(7(20 - y) + 5.50y) / (20 - y + y) = 5.95
Now, simplify and solve for y:
(140 - 7y + 5.50y) / 20 = 5.95
140 - 7y + 5.50y = 5.95 * 20
140 - 1.5y = 119
-1.5y = -21
y = 14
Now, substitute the value of y back into Equation 2 to find x:
x + 14 = 20
x = 6
Therefore, to keep the cost of the mixture consistent with the ingredients, you should use 6 pounds of Celine almonds and 14 pounds of Salinas almonds in the mixture.