Ratio Word Problems
with Solutions and Explanations -
Grade 9
Detailed solutions and full explanations to math word problems -
grade 9 are presented.
1. There are 600 pupils in a school. The ratio of boys to girls in this school is 3:5.
How many girls and how many boys are in this school?
Solution
In order to obtain a ratio of boys to girls equal to 3:5, the number of boys has to
be written as 3 x and the number of girls as 5 x where x is a common factor to
the number of girls and the number of boys. The total number of boys and girls is
600. Hence
3x + 5x = 600
Solve for x
8x = 600
x = 75
Number of boys
3x = 3 × 75 = 225
Number of girls
5x = 5 × 75 = 375
2. There are r red marbles, b blue marbles and w white marbles in a bag. Write the ratio of the
number of blue marbles to the total number of marbles in terms of r, b and w.
Solution
The total number of marbles is
, r+b+w
The total ratio of blue marbles to the total number of marbles is
r / (r + b + w)
3. The perimeter of a rectangle is equal to 280 meters. The ratio of its length to its width is 5:2.
Find the area of the rectangle.
Solution
If the ratio of the length to the width is 5:2, then the measure L of the length and and the
measure W of the with can be written as
L = 5x and W = 2x
We now use the perimeter to write
280 = 2(2L + 2W) = 2(5x + 2x) = 14x
Solve for x
280 = 14x
x = = 20
The area A of the rectangle is given by
A = L × W = 5x × 2x = 10x2 = 10×202 = 4000 square meters
4 The angles of a triangle are in the ratio 1:3:8. Find the measures of the three angles of this
triangle.
Solution
If the ratio of the three angles is 1:3:8, then the measures of these angles can be written as x, 3x
and 8x. Also the sum of the three interior angles of a triangle is equal to 180°. Hence
x + 3x + 8x = 180
Solve for x
12x = 180
with Solutions and Explanations -
Grade 9
Detailed solutions and full explanations to math word problems -
grade 9 are presented.
1. There are 600 pupils in a school. The ratio of boys to girls in this school is 3:5.
How many girls and how many boys are in this school?
Solution
In order to obtain a ratio of boys to girls equal to 3:5, the number of boys has to
be written as 3 x and the number of girls as 5 x where x is a common factor to
the number of girls and the number of boys. The total number of boys and girls is
600. Hence
3x + 5x = 600
Solve for x
8x = 600
x = 75
Number of boys
3x = 3 × 75 = 225
Number of girls
5x = 5 × 75 = 375
2. There are r red marbles, b blue marbles and w white marbles in a bag. Write the ratio of the
number of blue marbles to the total number of marbles in terms of r, b and w.
Solution
The total number of marbles is
, r+b+w
The total ratio of blue marbles to the total number of marbles is
r / (r + b + w)
3. The perimeter of a rectangle is equal to 280 meters. The ratio of its length to its width is 5:2.
Find the area of the rectangle.
Solution
If the ratio of the length to the width is 5:2, then the measure L of the length and and the
measure W of the with can be written as
L = 5x and W = 2x
We now use the perimeter to write
280 = 2(2L + 2W) = 2(5x + 2x) = 14x
Solve for x
280 = 14x
x = = 20
The area A of the rectangle is given by
A = L × W = 5x × 2x = 10x2 = 10×202 = 4000 square meters
4 The angles of a triangle are in the ratio 1:3:8. Find the measures of the three angles of this
triangle.
Solution
If the ratio of the three angles is 1:3:8, then the measures of these angles can be written as x, 3x
and 8x. Also the sum of the three interior angles of a triangle is equal to 180°. Hence
x + 3x + 8x = 180
Solve for x
12x = 180
