Candy costing 1.25 per kilogram was mixed with candy costing 1.65 per kilogram to produce 10 kilograms of a candy mixture worth 1.40 per kilogram. find how may kilograms of each was used.
solve
1.25x + 1.65(10-x) = 1.4(10)
To solve this problem, we can use the method of solving a system of linear equations. Let's assume that x kilograms of candy costing $1.25 per kilogram were used, and y kilograms of candy costing $1.65 per kilogram were used.
Given that the total amount of candy mixture is 10 kilograms, we can write the equation:
x + y = 10 ---> Equation 1
The total cost of the candy mixture can be calculated by multiplying the cost per kilogram with the total weight of each type of candy. We know that it is worth $1.40 per kilogram, so we can write the equation:
(1.25 * x) + (1.65 * y) = 1.40 * 10 ---> Equation 2
Now we have a system of equations:
x + y = 10 ---> Equation 1
(1.25 * x) + (1.65 * y) = 1.40 * 10 ---> Equation 2
To solve this system, we can use the method of substitution or elimination. In this case, let's use the method of elimination.
Multiply Equation 1 by 1.65 to make the coefficients of y in both equations the same:
1.65 * (x + y) = 1.65 * 10
1.65x + 1.65y = 16.5 ---> Equation 3
Now subtract Equation 2 from Equation 3 to eliminate the variable y:
(1.65x + 1.65y) - ((1.25x) + (1.65y)) = 16.5 - (1.4 * 10)
1.65x + 1.65y - 1.25x - 1.65y = 16.5 - 14
0.4x = 2.5
Divide both sides by 0.4 to solve for x:
x = 2.5 / 0.4
x ≈ 6.25
Now substitute x back into Equation 1 to solve for y:
6.25 + y = 10
y = 10 - 6.25
y ≈ 3.75
Therefore, approximately 6.25 kilograms of candy costing $1.25 per kilogram and approximately 3.75 kilograms of candy costing $1.65 per kilogram were used to produce a 10-kilogram candy mixture worth $1.40 per kilogram.