While at a picnic, 42 adults drank iced tea, 24 adults drank bottled water, and 36 adults drank lemonade. What's the ratio, as a simplified fraction, of the number of adults who drank iced tea to the number of adults who drank either water or lemonade?
A) $7 / 10$
B) $6 / 11$
C) $4 / 13$
D) $7 / 17$
Answer (2)
Calculate the total number of adults who drank water or lemonade: 24 + 36 = 60 .
Express the ratio of iced tea drinkers to water or lemonade drinkers as a fraction: 60 42 .
Simplify the fraction by dividing both numerator and denominator by their greatest common divisor (GCD), which is 6: 60 ÷ 6 42 ÷ 6 = 10 7 .
The simplified ratio is 10 7 .
Explanation
Understanding the Problem Let's break down this problem. We need to find the ratio of adults who drank iced tea to those who drank either water or lemonade. First, we'll find the total number of adults who drank either water or lemonade. Then, we'll express the ratio as a fraction and simplify it.
Calculate the Total Number of Adults Who Drank Water or Lemonade To find the number of adults who drank either water or lemonade, we add the number of adults who drank water and the number of adults who drank lemonade:
24 + 36 = 60
Express the Ratio as a Fraction Now, we express the ratio of the number of adults who drank iced tea to the number of adults who drank either water or lemonade. The number of adults who drank iced tea is 42, and the number of adults who drank either water or lemonade is 60. So, the ratio is:
60 42
Simplify the Fraction To simplify the fraction, we find the greatest common divisor (GCD) of 42 and 60. The GCD of 42 and 60 is 6. Now, we divide both the numerator and the denominator by 6:
60 ÷ 6 42 ÷ 6 = 10 7
State the Final Answer So, the simplified ratio of the number of adults who drank iced tea to the number of adults who drank either water or lemonade is 10 7 .
Examples
Ratios are used in everyday life, such as when cooking to scale recipes up or down. For example, if a recipe calls for a ratio of 2 parts water to 1 part rice, understanding ratios helps you adjust the quantities correctly whether you're cooking for one person or a large group. In this problem, we used ratios to compare the number of people who preferred iced tea to those who preferred other beverages at a picnic, which is useful for planning future events.
The simplified ratio of the number of adults who drank iced tea to those who drank either water or lemonade is 10 7 . The chosen multiple choice option is A) 10 7 .
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