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Lesson Example Discussion Quiz: Class Homework

Step-1

Title: Ratio

Grade: 6-a Lesson: S3-L8

Explanation: Let us verify the answer here with the steps.

Lesson Steps Head1

Step	Type	Explanation	Answer
1	Problem	Mr. Peeter bought some oranges and pears. After giving away 20 oranges, he had twice as many pears as oranges left. If he had 32 pears in the end, what was the ratio of oranges to pears in the beginning?
2	Step	Let’s denote the number of oranges Mr. Peeter bought as O and the number of pears as P.
3	Step	After giving away 20 oranges, he had twice as many pears as oranges left	\$"P" = 2 times ("O" − 20)\$
4	Step	In the end, he had 32 pears	P = 32
5	Step	Set up an equation using these two steps of information	\$2 times ("O" − 20) = 32\$
6	Step	After simplification, the quantity of oranges "O" Mr.Peeter bought is	⇒ 2O − 40 = 32 ⇒ 2O = 72 ⇒ O = 36
7	Step	Now, to find the ratio of oranges to pears in the beginning, we can use the values of O and P	\$"Ratio" = "Oranges"/"Pears" = 36/32\$
8	Step	Simplify the ratio by dividing it by 4	\$"Ratio" = 9/8\$
9	Step	Therefore, the ratio of oranges to pears in the beginning was 9:8.
10		Answer	A

Step

Type

Explanation

Answer

Problem

Mr. Peeter bought some oranges and pears. After giving away 20 oranges, he had twice as many pears as oranges left. If he had 32 pears in the end, what was the ratio of oranges to pears in the beginning?

Step

Let’s denote the number of oranges Mr. Peeter bought as O and the number of pears as P.

Step

After giving away 20 oranges, he had twice as many pears as oranges left

\$"P" = 2 times ("O" − 20)\$

Step

In the end, he had 32 pears

P = 32

Step

Set up an equation using these two steps of information

\$2 times ("O" − 20) = 32\$

Step

After simplification, the quantity of oranges "O" Mr.Peeter bought is

⇒ 2O − 40 = 32

⇒ 2O = 72

⇒ O = 36

Step

Now, to find the ratio of oranges to pears in the beginning, we can use the values of O and P

\$"Ratio" = "Oranges"/"Pears" = 36/32\$

Step

Simplify the ratio by dividing it by 4

\$"Ratio" = 9/8\$

Step

Therefore, the ratio of oranges to pears in the beginning was 9:8.

Answer