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Lesson Example Discussion Quiz: Class Homework

Step-1

Title: Ratios

Grade: 8-a Lesson: S2-L2

Explanation: TODO

Description:

Explanation	Answer
Problem	The monthly incomes of two persons are in the ratio of 5:6, and their monthly expenditures are in the ratio of 7:9. If each saves $54 per month, find the monthly income of the 2nd person.
Operator used	:
Step - 1	According to the problem, the ratio of two incomes = 5:6 expenditure ratio = 7:9
Step - 2	Income of first person = \$5x\$
Step - 3	Income of second person = \$6x\$
Step - 4	We know that Expenditure = Income - Savings
Step - 5	Expenditure of first person = \$5x - 54\$
Step - 6	Expenditure of second person = \$6x - 54\$
Step - 7	So, we have \$(5x - 54) : (6x - 54) = 7:9\$
Step - 8	Use cross product rule, \$9(5x - 54) = 7(6x - 54)\$ ⇒ \$45x - 486 = 42x - 378\$ ⇒ \$\cancel3^1x = \cancel108^36\$ ⇒ \$x = 36\$
Step - 9	Then the income of the 2nd person is 6x = 6(36) = 108

Explanation

Answer

Problem

The monthly incomes of two persons are in the ratio of 5:6, and their monthly expenditures are in the ratio of 7:9. If each saves $54 per month, find the monthly income of the 2nd person.

Operator used

Step - 1

According to the problem,

the ratio of two incomes = 5:6

expenditure ratio = 7:9

Step - 2

Income of first person = \$5x\$

Step - 3

Income of second person = \$6x\$

Step - 4

We know that Expenditure = Income - Savings

Step - 5

Expenditure of first person = \$5x - 54\$

Step - 6

Expenditure of second person = \$6x - 54\$

Step - 7

So, we have \$(5x - 54) : (6x - 54) = 7:9\$

Step - 8

Use cross product rule,

\$9(5x - 54) = 7(6x - 54)\$

⇒ \$45x - 486 = 42x - 378\$

⇒ \$\cancel3^1x = \cancel108^36\$

⇒ \$x = 36\$

Step - 9

Then the income of the 2nd person is 6x = 6(36) = 108