Ratio Algebra Word Problem Game

Ratio Algebra Word Problem Quiz/Game
This game focuses on solving word problems involving Ratios. Ratio problems including currency exchange, chemistry concentrations, engineering scales, agricultural yields, and sports statistics. Scroll down the page for a more detailed explanation.

 

 

How to Play the Ratio Algebra Explorer Game

1. Look at the Problem: Read the problem carefully. Solve it and select one of the answers.
   
2. Check Your Work: If you selected the right answer, it will be highlighted in green. If you are wrong, it will be highlighted in red and the correct answer will be highlighted in green. A hint will be given to help you find the correct answer.
   
3. Get a New Problem: Click “Next Question” for a new problem.
   Your score is tracked, showing how many you’ve gotten right.
   
4. Finish Game When you have completed 10 questions, your final score will be displayed.
    
   

How to Solve Ratio Algebra Word Problems
Solving ratio algebra word problems is all about translating words into a mathematical equation. Once you understand the relationship between the parts and the whole, these problems become much more manageable.
The cross-multiply method (sometimes called the “Butterfly Method”) can be used to solve ratio problems where you have two equivalent fractions and one unknown value.

The Setup: “Label and Line Up”
The most important part of cross-multiplying is making sure your units match on both sides.
\(\frac{\text{Category A}}{\text{Category B}} = \frac{\text{Category A}}{\text{Category B}}\)
If you put “Apples” on top and “Cost” on the bottom for the first ratio, you must do the same for the second.

Step-by-Step Method
Follow these four steps to solve any standard ratio problem:

1. Write the first ratio as a fraction using the known values.
   
2. Write the second ratio as a fraction, using $x$ for the unknown value.
   
3. Cross-multiply: Multiply the numerator of the first by the denominator of the second, and vice versa.
   
4. Solve the resulting equation.
    
   

Worked Example:
Scaling a Recipe
Problem: A recipe uses 3 cups of flour for every 2 cups of sugar. If you decide to use 10 cups of flour, how much sugar do you need?
Step 1: Set up the Proportion
Identify your “Base Ratio” (3:2) and your “New Ratio” (10:x).
\(\frac{3 \text{ flour}}{2 \text{ sugar}} = \frac{10 \text{ flour}}{x \text{ sugar}}\)
Step 2: Cross-Multiply
Multiply diagonally across the equals sign:
3 × x = 3x
2 × 10 = 20
This gives you the equation:
3x = 20
Step 3: Solve for x
Divide both sides by 3:
\(x = \frac{20}{3}\)
x = 6.67 cups of sugar

Solving Complex Algebraic Ratios
Sometimes the problem involves a “change” (e.g., adding more items). In these cases, you use x as a common multiplier first, then cross-multiply the new relationship.
Example: Jan and Kim have marbles in the ratio 5:6. Jan gets 2 more marbles and the new ratio is 7:8.
Original amounts: Jan = 5x, Kim = 6x.
New Ratio setup: \(\frac{5x + 2}{6x} = \frac{7}{8}\)
Cross-multiply: 8(5x + 2) = 7(6x)
Solve:
40x + 16 = 42x
16 = 2x
x = 8
Final Answer: Initially, Jan had 5(8) = 40 and Kim had 6(8) = 48.
 

This video gives a clear, step-by-step approach to explain how to solve ratio algebra word problems using cross multiplication.

• Show Video

 

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