Question #d8432

1 Answer
Feb 11, 2017

Answer:

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

Explanation:

Note that #2 1/2 + 1 1/2 -> 5/2+3/2=4#

#color(red)("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 #" "5/2C_g+3/2C_o=4C_b=$12.5" "......Equation(1)#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("How to solve a variant on the given question")#

Just plucking a value out of the air:

Suppose that #C_g=2C_o" "....Equation(2)#

#color(magenta)("Solving for "C_o)#

Using #Equation(2)# substituting for #C_g# in #Equation(1)# 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 #" "larr" approximate value"#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(magenta)("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" in "Equation(1)#

#5/2C_g+" "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"#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~