The ratio $x: y$ is $1: 5$. Which two of the following statements are correct?
A. $y$ is $\frac{5}{6}$ of $x$
B. $x$ is $\frac{1}{5}$ of $y$
C. $x$ is $\frac{1}{6}$ of $y$
D. $y$ is $\frac{5}{6}$ of $(x+y)$
Answer (1)
The ratio x : y = 1 : 5 implies y x = 5 1 , which can be rewritten as x = 5 1 y and y = 5 x .
Evaluate statement A: y = 6 5 x is incorrect because y = 5 x .
Evaluate statement B: x = 5 1 y is correct.
Evaluate statement C: x = 6 1 y is incorrect because x = 5 1 y .
Evaluate statement D: y = 6 5 ( x + y ) is correct because substituting x = 5 1 y simplifies to y = y .
The two correct statements are B , D .
Explanation
Understanding the Problem We are given the ratio x : y = 1 : 5 . This means that y x = 5 1 . We need to determine which two of the given statements are correct.
Expressing x and y From the given ratio, we can write x = 5 1 y and y = 5 x . Now we will evaluate each statement.
Evaluating Statement A Statement A: y = 6 5 x . Since y = 5 x , this statement is incorrect.
Evaluating Statement B Statement B: x = 5 1 y . This is the same as x : y = 1 : 5 , so this statement is correct.
Evaluating Statement C Statement C: x = 6 1 y . Since x = 5 1 y , this statement is incorrect.
Evaluating Statement D Statement D: y = 6 5 ( x + y ) . Substitute x = 5 1 y into the equation: y = 6 5 ( 5 1 y + y ) = 6 5 ( 5 6 y ) = y . This statement is correct.
Final Answer Therefore, the two correct statements are B and D.
Examples
Understanding ratios is crucial in everyday life. For instance, when baking, a recipe might call for a flour-to-sugar ratio of 1:5. If you're using 1 cup of flour, you'll need 5 cups of sugar. Similarly, in mixing cleaning solutions, a concentrate might need to be diluted with water in a 1:5 ratio. This means for every 1 part of concentrate, you add 5 parts of water. Ratios help maintain the correct proportions, ensuring the desired outcome, whether it's a delicious cake or an effective cleaning solution.
