Questions on how to find maths ratios in different situations are presented along with detailed step-by-step solutions and explanations.
Questions and Step-by-Step Solutions
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Question 1: In the figure below are three different shapes: squares, triangles, and circles.

Use the above picture to find the following ratios:
- the ratio of the number of triangles to the number of circles
- the ratio of the number of circles to the number of squares
- the ratio of the number of triangles to total number of shapes
- the ratio of the number of circles to total number of shapes
- the ratio of the number of circles to number of triangles
► View Step-by-Step Solution
Based on the image counts, there are 9 triangles, 6 circles, and 3 squares (Total = 18 shapes).
A) Triangles to circles = 9 to 6
B) Circles to squares = 6 to 3
C) Triangles to total shapes = 9 to 18
D) Circles to total shapes = 6 to 18
E) Circles to triangles = 6 to 9
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Question 2: There are 15 apples, 10 bananas, and 5 pears in a basket. Use the given information to find the following ratios:
- the ratio of the number of bananas to the total number of fruits
- the ratio of the number of pears to the number of apples
- the ratio of the number of bananas to the number of apples
- the ratio of the number of pears to the total number of fruits
- the ratio of the number of apples to the total number of fruits
► View Step-by-Step Solution
Total fruits = 15 (apples) + 10 (bananas) + 5 (pears) = 30 fruits.
A) Bananas to total fruits = 10 to 30
B) Pears to apples = 5 to 15
C) Bananas to apples = 10 to 15
D) Pears to total fruits = 5 to 30
E) Apples to total fruits = 15 to 30
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Question 3: In a school, there are 120 boys and 180 girls. 40 of the boys are under 10 years and 140 of the girls are under 10 years. Use the given information to find:
- the ratio of the number of boys to the number of girls
- the ratio of the number of boys who are less than 10 to the number of boys who are 10 or older (in simplest form)
- the ratio of the number of girls who are less than 10 to the number of boys who are 10 or older (in simplest form)
- the ratio of the number of girls who are 10 or older to the total number of pupils (in simplest form)
- the ratio of the number of girls who are less than 10 to the total number of pupils who are 10 or older (in simplest form)
► View Step-by-Step Solution
Given Data:
- Total boys = 120 (40 under 10, so \(120 - 40 = 80\) boys are 10 or older)
- Total girls = 180 (140 under 10, so \(180 - 140 = 40\) girls are 10 or older)
- Total pupils = \(120 + 180 = 300\)A) Boys to girls = \(120 : 180 = 2 : 3\) (or 2 to 3)
B) Boys < 10 to boys \(\ge\) 10 = \(40 : 80 = 1 : 2\) (or 1 to 2)
C) Girls < 10 to boys \(\ge\) 10 = \(140 : 80 = 7 : 4\) (or 7 to 4)
D) Girls \(\ge\) 10 to total pupils = \(40 : 300 = 2 : 15\) (or 2 to 15)
E) Girls < 10 to total pupils \(\ge\) 10 (boys \(\ge\) 10 [80] + girls \(\ge\) 10 [40] = 120) = \(140 : 120 = 7 : 6\) (or 7 to 6)
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Question 4: Let \(a\), \(b\), and \(c\) be the number of blue, yellow, and white marbles in a box, respectively. Given that \(a > b\) and \(b > c\), answer True or False to the following statements:
- The ratio of blue marbles to the total number of marbles is less than the ratio of white marbles to the total number of marbles.
- The ratio of yellow marbles to the total number of marbles is greater than the ratio of blue marbles to the total number of marbles.
- The ratio of white marbles to the total number of marbles is less than the ratio of blue marbles to the total number of marbles.
► View Step-by-Step Solution
Total marbles = \(a + b + c\).
A) Ratio of blue to total is \(\dfrac{a}{a+b+c}\), and white to total is \(\dfrac{c}{a+b+c}\). Since \(a > c\), \(\dfrac{a}{a+b+c} > \dfrac{c}{a+b+c}\). Thus, the statement is False (F).
B) Ratio of yellow to total is \(\dfrac{b}{a+b+c}\), and blue to total is \(\dfrac{a}{a+b+c}\). Since \(b < a\), \(\dfrac{b}{a+b+c} < \dfrac{a}{a+b+c}\). Thus, the statement is False (F).
C) Ratio of white to total is \(\dfrac{c}{a+b+c}\), and blue to total is \(\dfrac{a}{a+b+c}\). Since \(c < a\), \(\dfrac{c}{a+b+c} < \dfrac{a}{a+b+c}\). Thus, the statement is True (T).