Question

Question #d8432

Answer 1

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)`

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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`
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`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"`
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`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"`
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