A mixture of water and sucrose is 10% sucrose by weight. How many grams of pure sucrose must be added to a 200-gram sample of this mixture to produce a mixture that is 20% sucrose?

Your original 10%, 200 g mixture has 180 g of water and 20 g of sucrose. Let x be the number of grams of sucrose you need to add. The reqiuorement is

(20 + x)/180 + x) = 0.20

Solve for x

But, aren't we adding the x grams to the original 200 ?

so I would say:
20+x = .2(200+x)
for x = 25

To solve this problem, we can set up a system of equations.

Let's denote the amount of pure sucrose to be added as "x" grams.

Given:
- The initial mixture is 10% sucrose by weight, meaning that the 200-gram sample contains 10% or 0.10 * 200 = 20 grams of sucrose.
- We need to add "x" grams of pure sucrose.
- The resulting mixture should be 20% sucrose by weight.

Equation 1: The amount of sucrose in the initial mixture plus the amount of sucrose added equals the amount of sucrose in the resulting mixture:
20 grams + x grams = (200 + x) grams * 0.20

To solve for "x," we can simplify Equation 1 and solve for "x":

20 + x = 0.20(200 + x)
20 + x = 40 + 0.20x
0.80x = 20
x = 20 / 0.80
x = 25

Therefore, 25 grams of pure sucrose must be added to the 200-gram sample to produce a mixture that is 20% sucrose.

To solve this problem, we need to find the number of grams of pure sucrose that must be added to the original mixture. Here's how you can do it step by step:

1. Determine the initial amount of sucrose in the 200-gram sample of the mixture. Since the mixture is 10% sucrose by weight, we can calculate it by multiplying the weight of the sample (200 grams) by the percentage of sucrose (10%):

Initial sucrose = 200 grams * 10% = 200 grams * 0.10 = 20 grams

So, the initial mixture contains 20 grams of sucrose.

2. Let's assume x grams of pure sucrose need to be added.

3. After adding x grams of pure sucrose, the total weight of the mixture will be 200 + x grams.

4. Since we want the final mixture to be 20% sucrose, we can set up the following equation:

(20 grams + x grams) / (200 grams + x grams) = 20%

5. We can now solve this equation to find x, the number of grams of pure sucrose that must be added. First, let's convert the percentage to a decimal:

20% = 0.20

(20 + x) / (200 + x) = 0.20

6. Cross multiplying the equation, we get:

0.20 * (200 + x) = 20 + x

40 + 0.20x = 20 + x

0.20x - x = 20 - 40

-0.80x = -20

Divide both sides by -0.80 to solve for x:

x = -20 / -0.80 = 25

Therefore, 25 grams of pure sucrose must be added to the 200-gram sample of the mixture to produce a mixture that is 20% sucrose.