Lesson Example Discussion Quiz: Class Homework |
Step-5 |
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 |
Two numbers are in the ratio 3 : 2. If 2 is added to the first and 6 is added to the second number, they are in the ratio 4 : 5. Find the numbers. |
|
2 |
Hint |
Operator used : Ratio |
: |
3 |
Step |
Ratio of the two numbers |
3:2 |
4 |
Step |
Let us consider the two numbers as |
3x and 2x |
5 |
Step |
Number that is added to the first number |
2 ⇒ 3x + 2 |
6 |
Step |
Number that is added to the second number |
6 ⇒ 2x + 6 |
7 |
Step |
After adding the numbers, the ratio will be |
4:5 |
8 |
Step |
According to the problem |
\$(3x+2)/(2x+6)\$ = \$4/5\$ ⇒ \$5(3x+2)\$ = \$4(2x+6)\$ ⇒ \$15x+10)\$ = \$8x+24)\$ ⇒ \$15x - 8x\$ = \$24 - 10\$ ⇒ \$7x\$ = \$14\$ ⇒ \$x\$ = \$14/7\$ ⇒ \$x\$ = \$2\$ |
9 |
= |
\$x=2\$ |
|
10 |
Step |
The numbers are |
3x = 3 x 2 = 6 2x = 2 x 2 = 4 |
11 |
Step |
Therefore, the numbers are |
6 and 4 |
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