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Mixture & Money Problems Algebra Honors

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. 10 d +. 05 n = 1. 70 BACK

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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 5 A + 3 C = 196 BACK

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

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. 30(12)= 3. 6. 20 x +. 50 y =. 30(12) BACK

-2 10 x + y = 12. 20 x +. 50 y = 3. 6 2 x + 5 y = 36 -2 x – 2 y = -24 x + (4) = 12 x=8 8 gallons of 20% 4 gallons of 50% 3 y = 12 y=4 Check. 2(8) +. 5(4) = 3. 6 1. 6 + 2 = 3. 6 BACK

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.

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 x 3. 00 4. 00 Let’s fill in the chart with what we know. BACK

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 x 3. 00 3 x x+5 4. 00 Equation The equation comes from the vertical and horizontal totals. BACK

He will need 2. 5 lbs of the flavored coffee. BACK

An auto mechanic has 300 m. L 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% x 0% 300 + x 45% 180 0 Equation: 180 = 0. 45 (300 + x) BACK

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

Mixture & Money Problems Algebra Honors