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

Weight of dried bananas = 34.75 kg

Weight of dried apricot = 15.25 kg

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
`*` 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