Easy Math

2009-10-06 5:28 pm
1. A chemist is making a solution that is to be 55% chlorine. He has one solution that is 40% chlorine and another that is 65% chlorine. He wants 100 liters of the final solution. How much of each should he mix?
a. Choose a variable to represent the amount of the first solution. Then find the amount of the second solution to be added to make 100 liters. Now figure out how much chlorine is in each solution.
b. Write the equation.
c. Solve the equation
2. The Nut Barn needs 10 pounds of mixed peanuts and cashews to sell for $8.50 per pound. Cashews alone sell for $10 per pound and peanuts for $7.50 per pound. What is the amount of cashews that can be in the mixture and hold the price to $8.50 per pound.
a. Choose a variable to represent the number of pounds of peanuts. Then find the number of pounds of cashews to be added to make 10 pounds total. Now figure out the cost of the amount of each nut in the mixture.
b. Write the equation.
c. Solve the equation.
3. A solution containing 30% insecticide is to be mixed with a solution containing 50% insecticide to make 200 liters of a solution that is 42% insecticide. How much of the 30% solution can you use?
a. Choose a variable to represent the first solution and an expression to represent the second one.
b. Write the equation.
c. Solve the equation.
4. A 50 gallon barrel of milk is 4% butterfat. How much skim milk must be added to make a milk that is 1% butterfat?
a. Fifty gallons represents the amount of 4% butterfat milk. Choose a variable to represent the skimmed milk. Choose an expression to represent the final mixture.
b. Write the equation. This involves the amount of mixture times the percent of butterfat.
c. Solve the equation.
更新1:

5. A candy store mixes plain and peanut m&ms. The plain cost $2.50 per pound and the peanut cost $3.00 per pound. How many of each should they mix to make a 5 pound mixture that they can sell for $2.70 per pound.

更新2:

a. Choose a variable to represent the plain m&ms and an expression to represent the peanut m&ms. b. Write the equation. c. Solve the equation.

回答 (1)

2009-10-06 7:25 pm
✔ 最佳答案
Q1.
Let amount of 1st solution = x
Then amount of 2nd solution = 100 - x
Amount of chlorine in 1st solution = 40%x = 0.4x
Amount of chlorine in 2nd solution = 65%(100 - x) = 0.65(100 - x)
Total amount of chlorine = 0.4x + 0.65(100 - x)
which is required to be 55% of 100 liters = 55 liters, so
0.4x + 0.65(100 - x) = 55
0.4x + 65 - 0.65x = 55
10 = 0.25x
x = 10/0.25 = 40 liters= 1st solution, 60 liters = 2nd solution.
Q2.
Let weight of peanut = x
so weight of cashew nut = 10 - x
Amount of peanut = 7.5x
Amount of cashew nut = 10(10 - x)
Total amount = 7.5x + 10(10 -x) = amount of final product = (10)(8.5) = 85
7.5x + 100 - 10x = 85
2.5x = 15
x = 15/2.5 = 6 pounds of peanut and 4 pounds of cashew nut.
Remaining questions are similar that you can try yourself.



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