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A candy factory wants to make 1,530 liters of syrup that is 30% sugar. If only          syrup that is 16% sugar and one that is 50% sugar are in stock, how much of          the syrup with the lower concentration should be used?1 pointA. 520 litersB. 630 litersC. 900 litersD. 1, 010 litersClear selectionBackNext

Question

A candy factory wants to make 1,530 liters of syrup that is 30% sugar. If only          syrup that is 16% sugar and one that is 50% sugar are in stock, how much of          the syrup with the lower concentration should be used?1 pointA. 520 litersB. 630 litersC. 900 litersD. 1, 010 litersClear selectionBackNext

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Solution

To solve this problem, we can use the method of weighted averages.

Let's denote:

  • x as the amount of 16% sugar syrup
  • y as the amount of 50% sugar syrup

We know that the total amount of syrup is 1530 liters, so we have the equation:

x + y = 1530

We also know that the final syrup is 30% sugar, so we have the equation:

0.16x + 0.50y = 0.30 * 1530

Now we can solve this system of equations.

First, let's express y from the first equation:

y = 1530 - x

Now we can substitute y in the second equation:

0.16x + 0.50 * (1530 - x) = 0.30 * 1530 0.16x + 765 - 0.50x = 459 0.34x = 306 x = 306 / 0.34 x = 900

So, the factory should use 900 liters of the syrup with the lower concentration. The correct answer is C. 900 liters.

This problem has been solved

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