# Question d8432

Feb 11, 2017

There is a problem with this question. It has some information missing.

#### Explanation:

Note that $2 \frac{1}{2} + 1 \frac{1}{2} \to \frac{5}{2} + \frac{3}{2} = 4$

$\textcolor{red}{\text{There is no indication if the cost of one juice is different to the other}}$

You would solve it on the following lines:

Let the unit cost of grape juice be ${C}_{g}$
Let the unit cost of orange juice be ${C}_{o}$
Let the unit cost of the blend be ${C}_{b}$

Then we have $\text{ "5/2C_g+3/2C_o=4C_b=$12.5" } \ldots \ldots E q u a t i o n \left(1\right)$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ From this point on you would need to know the ratio of the cost of one type of juice to the other. On the other hand; if they are the same then each quart for each type costs the same as C_b = ($12.5)/4 = $3.125 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ $\textcolor{b l u e}{\text{How to solve a variant on the given question}}$Just plucking a value out of the air: Suppose that ${C}_{g} = 2 {C}_{o} \text{ } \ldots . E q u a t i o n \left(2\right)$$\textcolor{m a \ge n t a}{\text{Solving for } {C}_{o}}$Using $E q u a t i o n \left(2\right)$substituting for ${C}_{g}$in $E q u a t i o n \left(1\right)$giving: 5/2(2C_0)+3/2C_o=$12.50" "....Equation(1_a)

5C_0+3/2C_0=$12.50 13/2C_o=$12.50

C_o=2/13xx$12.50 larr" exact value" C_o~~$1.92 to 2 decimal places $\text{ "larr" approximate value}$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{m a \ge n t a}{\text{Solving for } {C}_{g}}$

I am only going to round off at the end to reduce rounding errors.

Using the determined value for ${C}_{0}$ substitute for ${C}_{o} \text{ in } E q u a t i o n \left(1\right)$

$\frac{5}{2} {C}_{g} + \text{ "3/2C_o" "=$12.5" }$becomes: 5/2C_g+3/(cancel(2))((cancel(2))/13xx$12.50)=$12.5 5/2C_g=$12.50-(3/13xx$12.50) C_g=2/5[$12.50-(3/13xx$12.50)] C_g=2/5xx$12.50(1-3/13)

C_g=$3 11/13 larr" as an exact value" C_g~~$3.85 larr" as an approximate value"#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~