Sienna has a bag of colored marbles. The bag contains 70 green marbles, 42 orange marbles, and 28 purple marbles. What are the ratios of the number of green marbles, orange marbles, and purple marbles, respectively, to the total number of marbles?
a) Green = 1 to 2 ; orange = 10 to 3 ; purple = 1: 5
b) Green = 1 to 2 ; orange = 3 to 10 ; purple = 1: 5
c) Green = 1 to 5 ; orange = 10 to 3 ; purple = 1: 2
d) Green = 1 to 5 ; orange = 3 to 10 ; purple = 1: 2
Answer (2)
Calculate the total number of marbles: 70 + 42 + 28 = 140 .
Calculate the ratio of green marbles: 140 70 = 2 1 .
Calculate the ratio of orange marbles: 140 42 = 10 3 .
Calculate the ratio of purple marbles: 140 28 = 5 1 .
The ratios are Green = 1 to 2 , Orange = 3 to 10 , Purple = 1 : 5 . The answer is b
Explanation
Find the total number of marbles First, let's find the total number of marbles in the bag. We have 70 green marbles, 42 orange marbles, and 28 purple marbles. Adding these together gives us the total number of marbles.
Calculate the total The total number of marbles is: 70 + 42 + 28 = 140 So, there are 140 marbles in total.
Calculate the ratio of green marbles Now, we need to find the ratio of each color to the total number of marbles. Let's start with the green marbles. The ratio of green marbles to the total is: 140 70 = 2 1 So, the ratio of green marbles to the total is 1 to 2.
Calculate the ratio of orange marbles Next, let's find the ratio of orange marbles to the total number of marbles. The ratio of orange marbles to the total is: 140 42 = 10 3 So, the ratio of orange marbles to the total is 3 to 10.
Calculate the ratio of purple marbles Finally, let's find the ratio of purple marbles to the total number of marbles. The ratio of purple marbles to the total is: 140 28 = 5 1 So, the ratio of purple marbles to the total is 1 to 5.
Compare and conclude Therefore, the ratios of green, orange, and purple marbles to the total number of marbles are 1 to 2, 3 to 10, and 1 to 5, respectively. Comparing these ratios to the given options, we find that option b) matches our calculated ratios.
Examples
Understanding ratios is very useful in everyday life. For example, if you're baking a cake and need to adjust the recipe, you use ratios to maintain the correct proportions of ingredients. If a recipe calls for a 2:1 ratio of flour to sugar, and you want to make a larger cake, you'll need to increase both the flour and sugar while keeping that ratio the same to ensure the cake turns out right. Similarly, ratios are used in mixing paints, calculating fuel efficiency in cars, and understanding financial statements.
The ratios of green, orange, and purple marbles to the total are 1 to 2, 3 to 10, and 1 to 5, respectively. Thus, the correct option is b) Green = 1 to 2; Orange = 3 to 10; Purple = 1:5.
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