1. The ratio of boys to girls in a classroom is 2:3. If there are 12 boys in the classroom, how many girls are there?
Solution:
The ratio of boys to girls is given as 2:3.
So, the ratio can be written as boys/girls = 2/3.
We are given that there are 12 boys.
Let the number of girls be x.
According to the given ratio, we can set up the equation:
12/x = 2/3.
Cross-multiplying, we get:
12 * 3 = 2 * x.
Simplifying, we have:
36 = 2x.
Dividing both sides by 2, we get:
18 = x.
Therefore, there are 18 girls in the classroom.
2. The ratio of the lengths of two sides of a rectangle is 3:4. If the length is 15 cm, what is the width of the rectangle?
Solution:
The ratio of the lengths of the sides is given as 3:4.
So, the ratio can be written as length/width = 3/4.
We are given that the length is 15 cm.
Let the width be x cm.
According to the given ratio, we can set up the equation:
15/x = 3/4.
Cross-multiplying, we get:
15 * 4 = 3 * x.
Simplifying, we have:
60 = 3x.
Dividing both sides by 3, we get:
20 = x.
Therefore, the width of the rectangle is 20 cm.
3. The ratio of the number of red marbles to the number of blue marbles in a jar is 5:2. If there are 35 red marbles, how many blue marbles are there?
Solution:
The ratio of red marbles to blue marbles is given as 5:2.
So, the ratio can be written as red/blue = 5/2.
We are given that there are 35 red marbles.
Let the number of blue marbles be x.
According to the given ratio, we can set up the equation:
35/x = 5/2.
Cross-multiplying, we get:
35 * 2 = 5 * x.
Simplifying, we have:
70 = 5x.
Dividing both sides by 5, we get:
14 = x.
Therefore, there are 14 blue marbles in the jar.
Representing Ratios Practice
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