Question

A baker has 10 ounces of 10% sugar syrup, but he wants
to strengthen it to a 70% syrup mixture. How much pure sugar
would he need to add?

Answer 1

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

Let's assume the baker needs to add x ounces of pure sugar to achieve the desired 70% sugar syrup mixture.

The amount of sugar in the original 10% syrup is 10% of 10 ounces = 1 ounce.

The amount of sugar in the final 70% syrup mixture will be (10 + x) ounces.

According to the method of mixtures, the amount of sugar in the final mixture should be equal to the sum of the sugar in the original mixture and the pure sugar added. So we can set up the equation:

1 + x = 0.7(10 + x)

Now let's solve for x:

1 + x = 7 + 0.7x

0.3x = 6

x = 20

Thus, the baker would need to add 20 ounces of pure sugar to achieve the desired 70% syrup mixture.