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

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