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Mixture Problem Solving quiz

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  • What is a mixture problem in algebra?
    A mixture problem involves combining two or more quantities to form a total amount, such as coins or solutions.
  • How do you represent the value of dimes and nickels in an equation?
    Multiply the number of dimes by \$0.10 and the number of nickels by \$0.05, then sum the results.
  • What is the first step in solving a mixture problem?
    Build an equation that sums the parts of the mixture to equal the total amount.
  • How do you handle equations with two variables in mixture problems?
    Express one variable in terms of the other using information from the problem, then substitute.
  • If Miles has eight more nickels than dimes, how is this written algebraically?
    n = d + 8, where n is the number of nickels and d is the number of dimes.
  • What is the value of eight nickels in dollars?
    Eight nickels are worth \$0.40.
  • How do you isolate the variable in a mixture equation?
    Collect all variable terms on one side, all constants on the other, then divide to solve for the variable.
  • What is the number of dimes Miles has if 1.8 divided by 0.15 equals d?
    Miles has 12 dimes.
  • How many nickels does Miles have if he has 12 dimes?
    Miles has 20 nickels, since n = 12 + 8.
  • What is the general structure for solving mixture problems?
    Build an equation summing the parts, express in one variable, solve, and state the answer.
  • How do you convert a percent to a decimal in mixture problems?
    Divide the percent by 100; for example, 40% becomes 0.4.
  • What equation relates the total liters in a solution mixture problem?
    x + y = total liters, where x and y are the amounts of each solution.
  • How do you find the total acid in a solution mixture problem?
    Multiply the percent (as a decimal) by the total volume to get the total acid amount.
  • If a chemist needs 14 liters of 50% acid, how much acid is needed?
    7 liters of acid are needed, since 0.5 × 14 = 7.
  • How much of each solution should be mixed to get 14 liters of 50% acid from 40% and 70% solutions?
    Mix 9.33 liters of 40% solution and 4.66 liters of 70% solution.