Mixture Problems Linear Systems

A juice shop sells a blend of two types of juice, one at $4 per bottle and the other at $6 per bottle. The shop wants to make a 50-bottle blend that sells for $5 per bottle. How many bottles of each type of juice should be used?

• The correct answer is 25 bottles of $4 juice and 25 bottles of $6 juice.

• The correct answer is 40 bottles of $4 juice and 10 bottles of $6 juice.

• The correct answer is 20 bottles of $4 juice and 30 bottles of $6 juice.

• The correct answer is 15 bottles of $4 juice and 35 bottles of $6 juice.

Solve the following mixture problem: A chemist has 20 liters of a 30% acid solution. How many liters of a 50% acid solution should be added to obtain a 40% acid solution?

• 10

• 5

• 15

• 25

A bakery sells two types of bread, one at $3 per loaf and the other at $5 per loaf. The bakery wants to make a 100-loaf batch that sells for $4 per loaf. How many loaves of each type of bread should be used?

• 60 loaves of $3 bread and 40 loaves of $5 bread

• 30 loaves of $3 bread and 70 loaves of $5 bread

• 70 loaves of $3 bread and 30 loaves of $5 bread

• 50 loaves of $3 bread and 50 loaves of $5 bread

Solve the following mixture problem: A chemist has 15 liters of a 25% acid solution. How many liters of a 40% acid solution should be added to obtain a 30% acid solution?

• 3 liters

• 5 liters

• 20 liters

• 10 liters

An owner of a gourmet food store has two varieties of herbal tea, one that costs $40 per kilogram and another that costs $50 per kilogram. How many kg of each type are needed to make 20 kg of a blend worth $46 per kg?

• 12 kg @ $50/kg + 8 kg @ $40/kg

• 14 kg @ $50/kg + 6 kg @ $40/kg

A shop sells two kinds of nuts, one that costs $500 per kg and another that costs $540 per kg. How many kilograms of each type of nut should be mixed in order to have 40 kg of a mixture worth $525 per kilogram?

• 25 kg @ $540/kg + 15 kg @ $500/kg

• 10 kg @ $540/kg + 30 kg @ $500/kg

Mr James has coffee worth $400/kg that he wishes to mix with 20kg of coffee worth $700/kg to get a mixture that can be sold for $500/kg. How many kg of the cheaper coffee beans should he use?

• 20kg

• 40kg

• 30kg

• 60kg

Find the amounts of 20% salt solution and 8% salt solution that should be mixed together to make 500 ml of 15% salt solution.

• 291.67 ml of 20% salt solution,
  208.33 ml of 8% salt solution

• 280 ml of 20% salt solution,
  220 ml of 8% salt solution

• 208.33 ml of 20% salt solution,
  291.67 ml of 8% salt solution

• 220 ml of 20% salt solution,
  280 ml of 8% salt solution

• A

• B

• C

• D

A restaurant uses 1.2 kg of tuna at $125/kg and 2.4 kg of salmon at $200/kg to make combo sushi rolls. What should the price per kg be of the combo rolls?

• $168/kg

• $163/kg

• $57/kg

• $175/kg