store mixes a Brazilian coffee worth worth $10 per kilogram and a turkish coffee worth $13 per kilogram. The mixture is to sell for $12 per kilogram. Find out how much of each should be used to make a 420-kilogram mixture.
my calculations all came out super wrong
If there are x kg of Brazilian coffee, then the rest (420-x) is Turkish. So,
10x + 13(420-x) = 12*420
x = 140
Note that 140 is 1/3 of 420, meaning that it drags the price down 1/3 of the way from 13 to 10, or $12.
To solve this problem, we can use a system of linear equations. Let's assign variables to the unknown quantities:
Let x be the amount (in kilograms) of the Brazilian coffee,
And let y be the amount (in kilograms) of the Turkish coffee.
We can set up two equations based on the given information:
1) The total weight of the mixture is 420 kilograms:
x + y = 420
2) The cost of the mixture is $12 per kilogram:
(10x + 13y) / 420 = 12
To solve this system of equations, we can use the substitution method:
1) Rearrange the first equation to solve for one variable:
x = 420 - y
2) Substitute the expression for x into the second equation and solve for y:
(10(420 - y) + 13y) / 420 = 12
(4200 - 10y + 13y) / 420 = 12
(4200 + 3y) / 420 = 12
3) Simplify the equation:
4200 + 3y = 5040
3y = 5040 - 4200
3y = 840
y = 840 / 3
y = 280
4) Substitute the value of y back into the first equation to solve for x:
x + 280 = 420
x = 420 - 280
x = 140
So, you would need 140 kilograms of Brazilian coffee and 280 kilograms of Turkish coffee to make a 420-kilogram mixture.