Question

Hank has some 60% maple syrup and some 80% maple syrup in his restaurant. How manyounces of each should he use to make 100 ounces of 75% maple syrup?

Answer 1

Let x be the amount of used ounces of the 60% maple syrup and y the amount of used ounces of the 80% maple syrup.

We will mix this two quantities so we get 100 ounces. That is, we add both quantities to get 100 ounces, so we have the equation

$x+y=100$

Now, we want to find the second equation to find x and y. To do so, we will calculate the amount of maple we have.

In x ounces of the mixture, we would have

$0.6\cdot x$

of maple syrup.

For the other mixture, we would have

$0.8\cdot y$

The sum should be equal to the total amount of maple we have in the new mixture. Since we have a total of 100 ounces and a concentration of 75% we would have

$100\cdot0.75$

So, by adding the previous results and making it equal to this last amount, we get

$0.6\cdot x+0.8\cdot y=100\cdot0.75=75$

To avoid decimals, we can multiply this equation by 10, so we have

$6x+8y=750$

Using the first equation we can find that

$x=100\text{ -y}$

If we replace this value in the second equation, we get

$6\cdot(100\text{ -y)+8y=750}$

Distributing on the left side, we get

$600\text{ - 6y+8y=750}$

Operating on the left side, we get

$600+2y=750$

By subtracting 600 on both sides ,we get

$2y=750\text{ -600=150}$

By dividing both sides by 2 we get

$y=\frac{150}{2}=75$

If we replace this value in the equation we found for x, we get

$x=100\text{ -75 = 25}$

So, we need to mix 25 ounces of the first maple syrup and 75 ounces of the second one to get the desired mixture.