Question

20 kgs of fruits consisting of raspberries worth $6.00/kg , blue berries worth $2.50/kg and strawberries worth $1.50/kg are mixed.if there are twice as many blueberries as respberries and the total value of the fruits s $56.00 how maby of each fruits are there?

Answer 1

Given:

20 kgs of fruits consisting of raspberries worth $6.00/kg, blueberries worth $2.50/kg and strawberries worth $1.50/kg are mixed

If there are twice as many blueberries as raspberries and the total value of the fruits s $56.00

To find:

how many of each fruit are there?

Solution:

If we assume,

"x" kg → as the weight of blueberries

Then,

"2x" kg → will be the weight of the raspberries as we are given that there are twice as many blueberries as raspberries.

As the total weight of fruits is given as 20 kgs,

So, the weight of strawberries will be = 20 - (x + 2x) = (20 - 3x) kg

Now, according to the question, we can form an equation as:

$6x + [2.5 \times 2x] + [1.5 \times (20 - 3x)] = 56$

$\implies 6x + 5x + 30 - 4.5x = 56$

$\implies 6x + 5x - 4.5x = 56 - 30$

$\implies 6.5x = 26$

$\implies x = \frac{26}{6.5}$

$\implies x = 4$

∴ 2x = 2 × 4 = 8

and

∴ 20 - 3x = 20 - (3 × 4) = 20 - 12 = 8

Thus, there are,

$\boxed{\bold{Blueberries \rightarrow\: \underline{4\:kg}}}.\\\\\boxed{\bold{Raspberries \rightarrow\: \underline{8\:kg}}}.\\\\\boxed{\bold{Strawberries \rightarrow\: \underline{8\:kg}}}.$

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