How much water and sugar does…

Mathematics Questions

How much water and sugar does Anton need to make 5 lb of sugar syrup for each concentration: 50%, 5%, 75%, and 1.5%?

Short Answer

Anton needs to understand percent by mass to calculate the necessary amounts of sugar and water for making syrups with a total mass of 5 lbs. For different syrup concentrations (50%, 5%, 75%, and 1.5%), he can determine specific weights for sugar and water, and then mix them accordingly to ensure consistent sweetness and texture.

Step-by-Step Solution

Step 1: Understand Percent by Mass

To create sugar syrups, Anton needs to understand how to use percent by mass to determine the amounts of sugar and water required for each syrup concentration. This concept helps in calculating the proportion of sugar relative to the total mass of the syrup. In this case, the total mass of each syrup will be 5 lbs, which is crucial for accurate measurements.

Step 2: Calculate Ingredients for Each Syrup

Using the total mass of 5 lbs, Anton can calculate the required amounts of sugar and water for each syrup concentration. The calculations are based on the specified percentage of sugar in the syrup, as follows:

  • 50% Syrup: 2.5 lbs sugar and 2.5 lbs water
  • 5% Syrup: 0.25 lbs sugar and 4.75 lbs water
  • 75% Syrup: 3.75 lbs sugar and 1.25 lbs water
  • 1.5% Syrup: 0.075 lbs sugar and 4.925 lbs water

Step 3: Mix Ingredients Accordingly

Once Anton has the precise measurements for sugar and water, he can proceed to mix them according to the calculated values. Each type of syrup will require careful blending of the specified amounts to achieve the desired concentration. Proper mixing will ensure that the syrups have consistent sweetness and texture.

Related Concepts

Percent by mass

A measurement that expresses the concentration of a component as a percentage of the total mass of a solution or mixture.

Total mass

The overall weight of all components combined in a mixture, which is used to calculate proportions of ingredients.

Syrup concentration

The specific ratio of sugar to water in a syrup, often expressed as a percentage indicating how much sugar is present relative to the total mass of the syrup.

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