Question

A juice vendor prepares fruit juice by mixing apple juice and grape juice in the ratio of $5:3.$ The vendor takes an order to make $2\text{L}$ of fruit juice. Find the required quantity of grape juice using the graphical method.

• A. $750\text{L}$
• B. $750\text{mL}$
• C. $1.2\text{L}$

Answer 1

The correct option is B $750\text{mL}$

It is given that
$\frac{\text{Quantity of apple juice}}{\text{Quantity of grape juice}}=\frac{5}{3}$

Let, the quantity of apple juice and grape juice are represented by $x\text{L}$ and $y\text{L},$ respectively.

$\therefore \frac{x}{y}=\frac{5}{3}$
$\Rightarrow y=\frac{3}{5}x$
On comparing with slope-intercept form of line $y=mx+b$, we get:
$\Rightarrow \frac{\text{Rate of change of y}}{\text{Rate of change of x}}=\frac{3}{5}$

Total quantity of fruit juice $=2\text{L}$
$\Rightarrow x+y=2\text{L}$
In intercept form, the equation is
$\Rightarrow \frac{x}{2}+\frac{y}{2}=1$
Plotting this two equations we get,


$y=0.75\text{L}=750\text{mL}$
$\therefore$ Required amount of grape juice $750\text{mL}.$