susan wants to mix 10 pounds of virginia peanuts that cost $3.50 a pound with Spanish peanuts that cost $3.00 a pound to obtain a mixture that costs $3.40 a pound. How many pounds of Spanish peanuts should she use?
To solve this problem, we can set up an equation based on the given information.
Let's say Susan wants to mix x pounds of Spanish peanuts.
The cost of Virginia peanuts per pound is $3.50, so the cost of the Virginia peanuts used in the mixture is 10 pounds multiplied by $3.50, which is 10 * 3.50 = $35.
The cost of Spanish peanuts per pound is $3.00, so the cost of x pounds of Spanish peanuts used in the mixture is x pounds multiplied by $3.00, which is x * 3.00 = 3x.
The total cost of the mixture is given as $3.40 per pound. Since we have 10 pounds of Virginia peanuts and x pounds of Spanish peanuts, the total weight of the mixture is 10 + x pounds. Therefore, the total cost of the mixture is (10 + x) * $3.40.
According to the problem, the equation is:
35 + 3x = (10 + x) * 3.40
Now, let's solve the equation to find the value of x.
35 + 3x = 34 + 3.4x (simplified the right side of the equation)
3x - 3.4x = 34 - 35 (combined like terms)
-0.4x = -1 (subtracted)
x = -1 / -0.4 (divided)
x = 2.5
Therefore, Susan should use 2.5 pounds of Spanish peanuts to obtain the desired mixture.
let the amount of Spanish peanuts to be added be x lb
then 3.5(10) + 3x = 3.4(10+x)
solve for x