Question

How many liters of water must be added to 15 liters of 40 % sugar syrup to obtain 30
% sugar syrup?

Answer 1

To solve this problem, we need to determine how many liters of water to add to dilute a 40% sugar syrup to a 30% sugar syrup.

We start with 15 liters of a 40% sugar syrup. The amount of sugar in the syrup is calculated as follows:

\[
\text{Amount of sugar} = \text{Volume of syrup} \times \text{Concentration} = 15 \text{ liters} \times 0.40 = 6 \text{ liters of sugar}
\]

We want to find the volume of water \( x \) to add, so that the final concentration of sugar becomes 30%. The total volume of the new mixture will thus be:

\[
\text{Total volume} = 15 + x
\]

The 6 liters of sugar should now represent 30% of the total volume. This can be expressed with the equation:

\[
0.30 \times (15 + x) = 6
\]

Next, we solve for \( x \):

1. Distribute the 0.30:
\[
0.30 \times 15 + 0.30x = 6
\]
\[
4.5 + 0.30x = 6
\]

2. Subtract 4.5 from both sides:
\[
0.30x = 6 - 4.5
\]
\[
0.30x = 1.5
\]

3. Now, divide both sides by 0.30:
\[
x = \frac{1.5}{0.30} = 5
\]

Thus, the amount of water that needs to be added is **5 liters**.