Sarah wants to mix together some M&M's costing $5.00 per kilogram with some peanuts costing $7.50 per kilogram. She wants to sell 10kg of the mixture for $7.25 per kg. How many kilograms of M&M's are needed?
lets say she buys m killograms of M&M's, and p killograms of peanuts. we have:
5m+7.5p=72.5
m+p=10
5m+5p=50
2.5p=22.5
p=9
m+9=10
m=$\boxed{1}$
m = m&m kg cost $ 5 m
p = peanuts kg = 10-m cost $ 7.5 (10-m)
10 kg final amount cost 7.25 (10)
5m + 7.5 (10-m) = 7.25 (10)
-2.5 m = -2.5
m = 1 kg then p = 10 -m = 9 kg of peanuts