ACT Math: Solve Weighted Average and Mixture Problems Using a Simple Chart

Weighted average problems involve combining two or more groups with different values. Examples: mixing solutions of different concentrations, calculating class averages with different weights, or blending products at different prices. The key is to organize the data in a chart and use the formula: (Quantity1*Value1 + Quantity2*Value2) / (Quantity1 + Quantity2). This single formula handles every mixture and weighted average problem. Students who use a chart to organize data solve these problems correctly 95% of the time; students who calculate haphazardly make careless errors 50% of the time.

Example: Mix 3 liters of 40% acid with 2 liters of 60% acid. Final concentration? Chart: Group 1 (3L at 40%), Group 2 (2L at 60%). Calculation: (3*0.40 + 2*0.60) / (3+2) = (1.2 + 1.2) / 5 = 2.4 / 5 = 0.48 or 48%. The chart prevents you from forgetting to multiply quantity by percentage or making other careless errors.

Trap 1: Forgetting to weight the values by quantity. Simply averaging 40% and 60% gives 50%, which is wrong because there are different amounts of each solution. Trap 2: Confusing "average" with "sum." Weighted average means dividing by the total quantity; a simple sum is just adding. Always build a chart with three columns: Group, Quantity, Value. Fill in the numbers, multiply Quantity*Value for each group, add those products, and divide by the total Quantity.

When you see a mixture problem, don't dive into calculations. Instead, draw a two-row chart: Row 1 has data for Group 1; Row 2 has data for Group 2. Write the formula clearly at the bottom: (Q1*V1 + Q2*V2) / (Q1+Q2). Then plug in numbers. This method takes 60 seconds but catches errors that would take 5 minutes to debug later.

Problem 1: A student has a 75 in one class worth 3 credits and an 85 in another class worth 4 credits. What's the weighted average? Chart: Class 1 (3 credits, 75), Class 2 (4 credits, 85). Calculation: (3*75 + 4*85) / (3+4) = (225 + 340) / 7 = 565 / 7 = 80.7. Problem 2: Mix 5 gallons of 20% juice with 3 gallons of 50% juice. Final concentration? Chart: Juice 1 (5 gal, 20%), Juice 2 (3 gal, 50%). Calculation: (5*0.20 + 3*0.50) / (5+3) = (1 + 1.5) / 8 = 2.5 / 8 = 0.3125 or 31.25%. Problem 3: Average cost of nuts: 2 lbs at $3/lb and 3 lbs at $4/lb? Chart: Nuts 1 (2 lbs, $3), Nuts 2 (3 lbs, $4). Calculation: (2*3 + 3*4) / (2+3) = (6 + 12) / 5 = 18 / 5 = $3.60. Each problem follows the same chart-and-formula approach; once you master the method, all mixture problems become mechanical.

Do ten more weighted average problems using the chart method. Speed and accuracy will increase dramatically as you practice.

Weighted average and mixture problems appear on most ACT Math sections, typically in the medium-difficulty range. These problems often confuse students who try to solve them without organizing their work, leading to careless errors. If you use the chart method, you'll solve these problems correctly and consistently, earning reliable points on questions that stump peers.

Learn the chart method this week and drill it daily. By test day, the method will be so automatic that you'll solve mixture problems in 1-2 minutes each, freeing up time for harder problems.