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Mixture & Money Problems

This resource explores a variety of mixture and money-related algebra problems, showcasing methods for finding the number of coins, ticket sales, mixtures of alcohol solutions, and coffee blends. Example problems involve figuring out how many dimes and nickels make up a total of $1.70 with 22 coins, calculating the number of adult and children tickets sold for a movie, and determining the necessary amounts of different alcohol solutions to achieve a specific concentration. Each problem is broken down using counting and value equations to teach problem-solving skills.

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Mixture & Money Problems

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  1. Mixture & Money Problems Algebra Honors

  2. John has $1.70, all in dimes and nickels. He has a total of 22 coins. How many of each kind does he have? Let d = number of dimes Let n = number of nickels Counting equation d + n = 22 Value equation .10d + .05n = 1.70 BACK

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  4. Tickets to a movie cost $5.00 for adults and $3.00 for children. If tickets were bought for 50 people for a total of $196 how many adult tickets were sold and how many children tickets were sold? Let A = the number of Adult tickets sold. Let C = the number of children tickets sold. Counting Equation A + C = 50 Value Equation 5A + 3C = 196 BACK

  5. 23 + C = 50 A + C = 50 -3 5A + 3C = 196 C = 27 -3A – 3C = -150 23 Adults and 27 Children 2A = 46 A = 23 Check 5(23) + 3(27) = 196 115 + 81 = 196

  6. How much 20% alcohol solution and 50% alcohol solution must be mixed to get 12 gallons of 30% alcohol solution? Let x = amount of 20% Let y = amount of 50% Counting Equation x + y = 12 Value Equation .20x + .50y = .30(12) .30(12)= 3.6 BACK

  7. x + (4) = 12 x + y = 12 -2 .20x + .50y = 3.6 x = 8 10 2x + 5y = 36 8 gallons of 20% 4 gallons of 50% -2x – 2y = -24 3y = 12 y = 4 Check .2(8) + .5(4) = 3.6 1.6 + 2 = 3.6 BACK

  8. A typical mixture problem reads like this: Joe would like to mix 5 lbs of Columbian coffee costing $4.50 per pound with enough flavored coffee costing $3.00 per pound to make a mix worth $4.00 per pound. How many pounds of the flavored coffee should he take? Let x = amount of flavored coffee in pounds Mixture problems can be more easily solved by using a grid.

  9. Joe would like to mix 5 lbs of Columbian coffee costing $4.50 per pound with enough flavored coffee costing $3.00 per pound to make a mix worth $4.00 per pound. How many pounds of the flavored coffee should he take? 5 4.50 3.00 x 4.00 Let’s fill in the chart with what we know. BACK

  10. Now we fill in the remaining cells. Since we are mixing the two types of coffee the mix Amt will be x + 5. For total multiply amt times cost and place in total column 5 4.50 22.5 3.00 3x x x + 5 4.00 Equation The equation comes from the vertical and horizontal totals. BACK

  11. He will need 2.5 lbs of the flavored coffee. BACK

  12. An auto mechanic has 300 mL of battery acid solution that is 60% acid. He must add water to the solution to dilute it so that it is only 45% acid. How much water should he add? 300 60% 180 0% 0 x Equation 300 + x 45% Equation: 180 = 0.45 (300 + x) BACK

  13. A health food store sells a mixture of raisins and roasted nuts. Raisins sell for $3.50/kg and nuts sell for $4.75/kg. How many kilograms of each should be mixed to make 20 kg of this snack worth $4.00/kg? (Write Equation Only) BACK

  14. Mixture & Money Problems Algebra Honors

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