There are 18 girls in a class and the ratio of the number of girls and boys in class is [tex]$3: 2$[/tex]. Find the number of boys.
Answer (2)
We are given the number of girls is 18 and the ratio of girls to boys is 3 : 2 .
We set up the equation b 18 = 2 3 , where b is the number of boys.
We solve for b by cross-multiplying and dividing: b = 3 18 × 2 = 12 .
The number of boys in the class is 12 .
Explanation
Understanding the Problem We are given that there are 18 girls in a class and the ratio of girls to boys is 3 : 2 . We need to find the number of boys in the class.
Setting up the Equation Let g be the number of girls and b be the number of boys. We are given that g = 18 and the ratio b g = 2 3 .
Substituting the Value of g We can substitute the value of g into the ratio equation: b 18 = 2 3
Cross-Multiplying To solve for b , we can cross-multiply: 3 b = 18 × 2 3 b = 36
Solving for b Now, divide both sides by 3 to find the number of boys: b = 3 36 b = 12 Therefore, there are 12 boys in the class.
Final Answer Thus, the number of boys in the class is 12.
Examples
Understanding ratios is very useful in everyday life. For example, if you are baking a cake and the recipe calls for a ratio of 3 cups of flour to 2 cups of sugar, and you only want to make half the cake, you can use ratios to determine that you need 1.5 cups of flour and 1 cup of sugar. Ratios are also used in calculating proportions, scaling recipes, and understanding map scales.
The number of boys in the class is 12, based on the given ratio of girls to boys, which is 3:2. By setting up the equation and solving for boys, we find that with 18 girls, there are 12 boys. This calculation follows the principles of ratios and basic algebra.
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