Pecans that cost $28.50 per kilogram were mixed with almonds that cost $22.25 per kilogram. How many kilograms of each were used to make a 25 kilogram mixture costing $24.25 per kilogram? Show all work

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ranikashyab066 ranikashyab066 · Answer 1 · 2019-12-18T12:03:23+01:00

Answer:

The pecans used in the mixture = 8 kg

The almonds used in the mixture = 17 kg

Step-by-step explanation:

The cost of per kg of pecans = $28.50

The cost of per kg of almonds = $22.25

Now, total weight of mixture = 25 kg

Let us assume the weight of pecans in the mixture = m kg

So, the amount of almonds in the mixture = Total weight - Weight of Pecans

= (25 - m) kg

Now, cost of m kg pecans = m x ( cost of 1 kg pecans) = m x ( $ 28.50)

= 28.50 m

cost of (25- m) kg almonds = (25 -m) x ( cost of 1 kg almonds)

= (25 - m) x ( $ 22.25)

= 556.25 - 22.25 m

Total cost of 25 kg of mixture = 25 x ( $24.25) = $606.25

Now, Total Cost of (almonds + Pecans) = Total cost of mixture

⇒28.50 m + 556.25 - 22.25 m = $606.25

or,6.25 m = 50

or, m = 50/6.25 = 8

Hence, the pecans used in the mixture = m = 8 kg

And the almonds used in the mixture = (25 - m) = 25 - 8 = 17 kg