Question

Ella has 0.5 lb of sugar. How much water should she add to make the following concentrations? Tell Ella how much syrup she will have in each case.
75% syrup

Answer 1

To make a 75% syrup solution, we can use the formula for concentration:

\[
\text{Concentration (\%)} = \left( \frac{\text{mass of solute}}{\text{mass of solution}} \right) \times 100
\]

In this case, the solute is sugar (0.5 lb), and we need to find the total mass of the solution when the concentration is set to 75%.

Let \( x \) be the total mass of the solution. Given that the concentration of sugar is 75%, we can express this as:

\[
75\% = \frac{0.5 \text{ lb}}{x} \times 100
\]

Rearranging this gives:

\[
x = \frac{0.5 \text{ lb}}{0.75}
\]

Calculating the value of \( x \):

\[
x = \frac{0.5 \text{ lb}}{0.75} = \frac{0.5}{0.75} \approx 0.6667 \text{ lb}
\]

This means the total mass of the solution should be approximately 0.6667 lb.

To find out how much water Ella should add, we subtract the mass of the sugar from the total mass of the solution:

\[
\text{mass of water} = x - \text{mass of sugar} = 0.6667 \text{ lb} - 0.5 \text{ lb} \approx 0.1667 \text{ lb}
\]

Thus, Ella should add approximately 0.1667 lb of water to her sugar to achieve a 75% syrup solution.

The total mass of syrup she will have is approximately 0.6667 lb.