Question

Dried bananas sell at $4.59/kg and dried apricots sell at $6.59/kg. How many of kilograms of each should be used to make a mixture of 50 kg of dried fruit to sell for $5.20/kg. Solve for substitution or elimination

Answer 1

Answer:

Weight of dried bananas = 34.75 kg

Weight of dried apricot = 15.25 kg

Step-by-step explanation:

Given that:

Cost of dried bananas = $4.59 per kg

Cost of dried apricots = $6.59 per kg

Total weight of mixture = 50 kg

Sales price of dried fruit = $5.20 per kg

To find:

The weight of each type of dry fruit = ?

Solution:

Let weight of dried bananas = $x$ kg

Let weight of dried apricot = $y$ kg

$x+y=50 ...... (1)$

Total cost of dried bananas = Cost of dried bananas per kg multiplied by weight of dried bananas

Total cost of dried bananas = $4.59$x$

Total cost of dried apricots = Cost of dried apricots per kg multiplied by weight of dried apricots

Total cost of dried apricots = $6.59$y$

As per question statement,

Total cost of dry fruits = $5.20 $\times$ 50 = $260

$260 = 4.59x+6.59y......(2)$

Using substitution:

By equation (1):

$x = 50-y$

Putting in equation (2):

$260 = 4.59 (50-y)+6.59y\\\Rightarrow 2y = 260 - 229.5\\\Rightarrow y = 15.25\ kg$

$x = 50 - 15.25\\\Rightarrow x = 34.75\ kg$

Therefore, the answer is:

Weight of dried bananas = 34.75 kg

Weight of dried apricot = 15.25 kg