Lesson Example Discussion Quiz: Class Homework |
Step-3 |
Title: Ratios |
Grade: 8-a Lesson: S2-L4 |
Explanation: Let us verify the answer here with the steps. |
Description:
| Step | Type | Explanation | Answer |
|---|---|---|---|
1 |
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. |
|
2 |
Hint |
Operator used : Ratio |
: |
3 |
Step |
According to the problem |
The ratio of incomes of two persons = 5:6 Expenditure ratio = 7:9 |
4 |
Step |
Income of first person |
\$5x\$ |
5 |
Step |
Income of second person |
\$6x\$ |
6 |
Step |
We know that Expenditure |
Income - Savings |
7 |
Step |
Expenditure of first person |
\$5x - 54\$ |
8 |
Step |
Expenditure of second person |
\$6x - 54\$ |
9 |
Step |
So, we have |
\$(5x - 54) : (6x - 54) = 7:9\$ |
10 |
Step |
Use cross product rule, |
\$9(5x - 54) = 7(6x - 54)\$ ⇒ \$45x - 486 = 42x - 378\$ ⇒ \$\cancel3^1x = \cancel108^36\$ |
11 |
= |
\$x = 36\$ |
|
12 |
Step |
Then the income of the 2nd person is 6x = 6(36) |
108 |
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