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Lesson Example Discussion Quiz: Class Homework

Example

Title: Ratios

Grade: 8-a Lesson: S2-L3

Explanation: Here are some examples of the topic with images and steps in sequence.

Examples:

Example: 1a

The ratio of girls to boys in a chess club is 5 : 4. There are 32 boys. How many girls are there in the club?

Ratio of boys and girls = 5:4
Number of boys = 32
Number of girls = \$5/4 = x/32\$
⇒ \$5/\cancel4^1 = x/\cancel32^8\$ ⇒ \$x= 40\$

Explanation: In the above problem, the ratio of boys and girls in chess club is 5:4 and the number of boys is 32 and number of girls in chess club is 40.

Example: 2a

Jayden and Isabella share a reward of $40 in a ratio of 2 : 3. How much did Jayden get?

Ratio of reward Jayden and Isabella share = 2:3
Reward that Jayden and Isabella share = $40
Jayden’s share = 2x
Sum of the ratio ⇒ 2x + 3x = 5x
⇒ 5x = 40
⇒x = \$40/5\$ ⇒ x = 8
Hence, Jayden’s share = \$2 \times 8 = $16\$

Explanation: In the above problem, the ratio of reward Jayden and Isabella share is 2:3 and the reward that Jayden and Isabella share is $40. Jayden’s share is 2x and sum of the ratio is 5x. Hence, Jayden’s share amount is 2 x 8 = $16.

Example: 3a

Two numbers are in the ratio 10 : 11. Their sum is 168. Find the numbers.

Sum of two numbers = 168
Ratio of the two numbers = 10:11
Let the numbers be 10x and 11x ⇒ 10x + 11x = 168
⇒ 21x = 168 ⇒ x = 168/21 ⇒ 8
First number = 10x ⇒ \$10 \times 8\$ = 80
Second number = 11x ⇒ \$11 \times 8\$ = 88

Explanation: In the above problem, the sum of two numbers is 168 and the ratio of the two numbers is 10:11. Considering the two numbers as 10x and 11x, the first number is 10x ⇒ \$10 \times 8\$ = 80 and the second number is 11x ⇒ \$11 \times 8\$ = 88.