Question

Dina wants to make 15 3/4 cups of strawberry drink by mixing water and strawberry syrup with a ratio of 2 1/4 cup of water for every 3/4 cup of syrup. how much water and syrup will she need ro use?

Answer 1

Answer:

The water she need is $7\frac{7}{8} \ cups.$ and strawberry syrup $11\frac{13}{16}\ cups$.

Step-by-step explanation:

Given:

Dina wants to make 15 3/4 cups of strawberry drink by mixing water and strawberry syrup with a ratio of 2 1/4 cup of water for every 3/4 cup of syrup.

Now, to find the quantity of water and syrup she need to use.

As given in question ratio so:

Strawberry syrup = 2 1/4 = 9/4.

Water = 3/4.

Total cups of strawberry drink = 15 3/4 = 63/4.

Let the strawberry syrup be $\frac{9}{4} x$.

And let the water be $\frac{3}{4} x$.

According to question:

$\frac{9x}{4} + \frac{3x}{4}=\frac{63}{4}$.

On adding the fractions:

⇒$\frac{9x+3x}{4} =\frac{63}{4}$

⇒$\frac{12x}{4} =\frac{63}{4}$

Multiplying both sides by 4 we get:

⇒$12x=63$

Dividing both sides by 12 we get:

⇒$x=\frac{63}{12}$

Dividing numerator and denominator by 3 on R.H.S we get:

⇒$x=\frac{21}{4}$

Now, putting the value of $x$ on ratios:

Strawberry syrup =  $\frac{9}{4}\times x=\frac{9}{4}\times\frac{21}{4}$

                             =  $\frac{189}{16}$

                             =  $11\frac{13}{16}\ cups$  

Water = $\frac{3}{4}\times x =\frac{3}{4} \times\frac{21}{4}$

          = $\frac{63}{8}$

          = $7\frac{7}{8} \ cups.$

Therefore, the water she need is $7\frac{7}{8} \ cups.$ and strawberry syrup $11\frac{13}{16}\ cups$.