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Maths Exercices
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

If we mix 15 Kg. of coffee which costs 6.9 /Kg. with an unknown quantity of a coffee which costs 9.6/Kg., we get a mixture which costs 7.98/kg. What quantity of the second type of coffee would this mixture contain?
Solution =