Answer:
The water she need is
and strawberry syrup
.
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
.
And let the water be
.
According to question:
.
<em>On adding the fractions:</em>
⇒![\frac{9x+3x}{4} =\frac{63}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B9x%2B3x%7D%7B4%7D%20%3D%5Cfrac%7B63%7D%7B4%7D)
⇒![\frac{12x}{4} =\frac{63}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B12x%7D%7B4%7D%20%3D%5Cfrac%7B63%7D%7B4%7D)
<em>Multiplying both sides by 4 we get:</em>
⇒![12x=63](https://tex.z-dn.net/?f=12x%3D63)
<em>Dividing both sides by 12 we get:</em>
⇒![x=\frac{63}{12}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B63%7D%7B12%7D)
<em>Dividing numerator and denominator by 3 on R.H.S we get:</em>
⇒![x=\frac{21}{4}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B21%7D%7B4%7D)
Now, putting the value of
on ratios:
Strawberry syrup =
= ![\frac{189}{16}](https://tex.z-dn.net/?f=%5Cfrac%7B189%7D%7B16%7D)
=
Water = ![\frac{3}{4}\times x =\frac{3}{4} \times\frac{21}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B4%7D%5Ctimes%20x%20%3D%5Cfrac%7B3%7D%7B4%7D%20%5Ctimes%5Cfrac%7B21%7D%7B4%7D)
=
= ![7\frac{7}{8} \ cups.](https://tex.z-dn.net/?f=7%5Cfrac%7B7%7D%7B8%7D%20%5C%20cups.)
Therefore, the water she need is
and strawberry syrup
.