Joy needs to mix a 20% glucose solution with a 60% glucose solution to create 200 millileters of a 50% solution. How many millileters of each solution must Joy use?
To solve this problem, we can set up a system of equations based on the information given.
Let x represent the amount (in milliliters) of the 20% glucose solution.
Then, the amount of the 60% glucose solution will be 200 - x, since the total volume is 200 milliliters.
Now, we can set up the equation for the glucose content in the final solution.
0.20x + 0.60(200 - x) = 0.50(200)
Let's solve this equation step by step:
Step 1: Distribute 0.60 to (200 - x).
0.20x + 120 - 0.60x = 100
Step 2: Combine like terms.
-0.40x + 120 = 100
Step 3: Subtract 120 from both sides.
-0.40x = -20
Step 4: Divide both sides by -0.40 to isolate x.
x = 50
So, Joy needs to use 50 milliliters of the 20% glucose solution.
To find the amount of the 60% glucose solution, we can substitute the value of x into the equation:
200 - x = 200 - 50 = 150
Therefore, Joy needs to use 50 milliliters of the 20% glucose solution and 150 milliliters of the 60% glucose solution to create 200 milliliters of a 50% solution.