Mixture problems
Mixture problems are word problems where items or quantities of different values are mixed together and you have to determine some quantity (percentage, price,...) of the resulting mixture.
A nut farmer mixes some peanuts that sell for $2.50/lb with almonds that sell for $5/lb to make a 12-pound mixture worth $3/lb. How many pounds of peanuts were in the mixture?
2.50x+5(12-x)=3·12
2.5x+60-5x=36
60-36=5x-2.5x
24=2.5x
x=9.6
There were 9.6 pounds of peanuts.
If you mix 20kg of type A wheat, which costs €0.60/kg, with 60kg of type B wheat, which costs €0.80/kg, what is the price of the resulting mixture?
20 Kg.
of type A wheat costs 20·0.6 = 12 euros.
60 Kg. of type B wheat costs 50·0.8 = 48 euros.
The resulting mixture is: 80 Kg. of wheat with a price of 60 euros.
Each kg costs:
1000g of gold which is 90% pure is mixed with an amount of gold which is 75% pure. The purity of the resultant mixture is 85%. What quantity of the gold of 75% purity was added?
If the purity of the first quantity is 90% then it contains 900g of pure gold.
Name x to the amount of the second mixure, which will contain 0.75x pure golden.
After the mixure, he will have 1000+x gr of metal with 85% purity, that is 0.85(1000+x) gr. of pure golden.
That is
0.85(1000+x)=900 +0.75x ; 850+0.85x=900+0.75x ; 0.1x=50 ; x=500
Solution:
500 gr. were added