If 800 mL of a juice drink is 15% grape juice, how much grape juice should be added to make a drink that is 20% grape juice? Use the table below to help.
To solve this problem, we can use a table to organize the information:
| Juice | Amount (mL) | Grape Juice (mL) | %
| ------------- | ------------- | ---------------- | --
| Original | 800 | 120 | 15
| Additive | ? | x | 100 (since we are adding pure grape juice)
| Final Mixture | 800 + ? | 120 + x | 20
To find the amount of grape juice to be added, we need to calculate the unknown values.
Since we want the final drink to have a concentration of 20%, we know that:
(120 + x) / (800 + ?) = 20/100
To simplify the equation, we can multiply both sides by 5:
5 * (120 + x) = 20 * (800 + ?)
Now let's solve the equation:
To solve this problem, we can set up a proportion:
Let's x be the amount of grape juice (in mL) that needs to be added.
Since the initial volume of the juice drink is 800 mL and it is 15% grape juice, there are 0.15 * 800 = 120 mL of grape juice in the initial drink.
For the final drink with 20% grape juice, the total volume will be 800 + x mL, and the amount of grape juice in this drink will be 0.20 * (800 + x) mL.
We can set up the following proportion:
120 mL (initial grape juice) : 800 mL (initial total volume) = x mL (added grape juice) : (800 + x) mL (final total volume)
To solve for x, we can use cross-multiplication:
120 * (800 + x) = 800 * x
96000 + 120x = 800x
96000 = 800x - 120x
96000 = 680x
x = 96000 / 680
x ≈ 141.18 mL
Therefore, approximately 141.18 mL of grape juice should be added to the original drink to make a drink that is 20% grape juice.
Hmmmm.
Let V bet the volume added.
(800ml+V).2=800*.15+V
solve for V.