Final answer:
To find the percentage of sugar in the mixture, calculate the amount of sugar in each solution, combine and divide by the total volume of the solution, and multiply by 100. In this case, it is 36.25% (choice a).
Step-by-step explanation:
When mixing solutions with different concentrations, you determine the final concentration by taking into account the volume and concentration of each individual component. To find the percentage of sugar in the new mixture when mixing 1 liter of a 25% sugar solution with 3 liters of a 40% sugar solution, you first calculate the mass of the sugar in each solution and then combine this information.
In the 1-liter solution at 25%, there are 0.25 liters of sugar (since 25% of 1 liter is 0.25 liters). In the 3-liter solution at 40%, there are 1.2 liters of sugar (since 40% of 3 liters is 1.2 liters). Combining the two solutions yields a total of 4 liters of mixture with 1.45 liters of sugar (0.25 + 1.2 liters).
The percentage of sugar in the new mixture is calculated by dividing the amount of sugar by the total volume of the mixture and then multiplying by 100 to get a percentage:
1.45 liters sugar / 4 liters solution × 100% = 36.25%