Question

A recipe for sparkling grape juice 1 1/2 quarts of sparkling water and 3/4 of grape juice. How much sparkling water woild you need to mix with 9 quarts of grape juice. How much grape juice would you need to mix with 15/4 quarts of sparkling water?

Answer 1

According to the recipe the ratio of sparkling water to grape juice = 1 1/2 : 3/4.

Let us convert 1 1/2 into improper fraction and that is 3/2.

Now, 3/2: 3/4 or 3/2 ÷ 3/4 = 3/2 × 4/3 = 2/1 or 2:1.

Therefore, sparkling water quantity is two times of the quantity of grape juice.

Now, we need to find the number of quarts of sparkling water need to mix in 9 quarts of grape juice.

Since, sparkling water quantity is two times of the quantity of grape juice.

Therefore, we need 2 × 9 = 18 quarts of sparkling water to mix in 9 quarts of grape juice.

And now we need to find the number of quarts of grape juice would we need to mix with 15/4 quarts of sparkling water.

Therefore, we need 1/2 × 15/4 = 15/8 quarts of grape juice to mix with 15/4 quarts of sparkling water.

Answer 2

Answer:

a) $x = 18\,qt$, b) $y = 1\,\frac{7}{8}\,qt$

Step-by-step explanation:

a) The amount of sparkling water needed is determined by simple rule of three:

$x = \frac{9\,qt}{\frac{3}{4}\,qt}\times \frac{3}{2}\,qt$

$x = 12\times \frac{3}{2}\,qt$

$x = 18\,qt$

b) The amount of grape juice needed is found by simple rule of three:

$y = \frac{\frac{15}{4}\,qt}{\frac{3}{2}\,qt } \times \frac{3}{4}\,qt$

$y = \frac{30}{12}\times \frac{3}{4}\,qt$

$y = \frac{90}{48}\,qt$

$y = \frac{15}{8}\,qt$

$y = 1\,\frac{7}{8}\,qt$