Su Li has 13 kg of almonds costing $5 per kilogram. How many kilograms of cashews costing $12 per kg should be added to get a mixture of the two nut types costing $7:45 per kg?
5*13 + 12x = 7.45(13+x)
solve for x
5xurmom aoan
Ah, mixing nuts, are we? That's nuts! Let's crunch the numbers and find out!
So, Su Li has 13 kg of almonds at $5 per kg. That's a pretty nutty deal!
Now, let's say Su Li wants to add some cashews, which cost $12 per kg. We want to create a mixture that costs $7.45 per kg.
Let's assume Su Li adds x kg of cashews to the mixture. Now, we can set up an equation:
(13 kg * $5/kg) + (x kg * $12/kg) = (13 kg + x kg) * $7.45/kg
Now, let's solve for x:
65 + 12x = 7.45(13 + x)
Now, that might seem a little nutty, but we can simplify it!
65 + 12x = 96.85 + 7.45x
Subtracting 7.45x from both sides, we get:
4.55x = 31.85
To find x, we divide both sides by 4.55:
x = 7 kg (rounded to the nearest kg)
So, Su Li should add 7 kg of cashews to the mixture to get a nutty blend costing $7.45 per kg.
To solve this problem, we need to use a weighted average formula. Let's assume that Su Li wants to add x kg of cashews.
The total weight of the mixture will be 13 kg + x kg.
Now, let's calculate the average cost per kilogram for the mixture using the weighted average formula:
Average Cost = (Total Cost of Almonds + Total Cost of Cashews) / Total Weight of Mixture
The total cost of almonds = 13 kg * $5/kg = $65
The total cost of cashews = x kg * $12/kg = $12x
The total weight of the mixture = 13 kg + x kg
Therefore, the equation becomes:
$7.45 = ($65 + $12x) / (13 kg + x kg)
To solve for x, we multiply both sides of the equation by 13 kg + x kg:
($7.45) * (13 kg + x kg) = $65 + $12x
Now, we can simplify the equation:
96.85 + 7.45x = $65 + $12x
Combine like terms:
7.45x - $12x = $65 - $96.85
-4.55x = -$31.85
Divide both sides by -4.55 to isolate x:
x = -$31.85 / -4.55 ≈ 6.99 kg
Therefore, Su Li needs to add approximately 6.99 kg of cashews costing $12 per kilogram to get a mixture of the two nut types costing $7.45 per kilogram.