1) SIX MORE THAN FOUR TIMES A NUMBER IS LESS THAN FIVE TIMES THE NUMBER. FIND THE NUMBER.
2) THE DIFFERENCE BETWEEN THE SQUARES OF TWO CONSECUTIVE NUMBERS IS 141.FIND THE NUMBERS.
3) THE DIFFERENCE BETWEEN THE SQUARES OF TWO CONSECUTIVE EVEN NUMBERS IS 36 .FIND THE NUMBERS.
4) THE DIFFERENCE BETWEEN THE SQUARES OF TWO CONSECUTIVE ODD NUMBERS IS 56 .FIND THE NUMBERS.
5) THE SUM OF TWO NUMBERS IS 90.ONE THIRD OF THE LARGER NUMBER IS 9 MORE THAN TWICE THE SMALLER ONE. WHAT ARE THE NUMBERS?
Answers
Answer:
Appropriate Question No 1 :-
➦ Six more than four times a number is four less than five times the number. Find the number.
Given :-
- Six more than four times a number is four less than five times the number.
To Find :-
- What is the number.
Solution :-
Let, the number be x
According to the question,
⇒ 6 + 4x = 5x - 4
⇒ 6 + 4 = 5x - 4x
⇒ 10 = x
➠ x = 10
∴ The number is 10.
__________________________
Question No 2 :-
➦ The difference between the squares of two consecutive number is 141. Find the numbers.
Given :-
- The difference between the squares of two consecutive number is 141.
To Find :-
- What are the numbers.
Solution :-
Let, me consecutive number be x
Then,
★ First number = x
★ Second number = x + 1
According to the question,
⇒ (x + 1)² - (x)² = 141
⇒ (x + 1 + x)(x + 1 - x) = 141 [ a² - b² = (a + b)(a - b) ]
⇒ (2x + 1)(1) = 141
⇒ 2x + 1 = 141
⇒ 2x = 141 - 1
⇒ 2x = 140
⇒ x = 140/2
➠ x = 70
Hence, the required numbers are :
★ First number :-
⇒ x
➲ 70
★ Second number :-
⇒ x + 1
⇒ 70 + 1
➲ 71
∴ The number is 70 and 71.
__________________________
Question No 3 :-
➦ The difference between the squares of two consecutive even number is 36. Find the numbers.
Given :-
- The difference between the squares of two consecutive even number is 36.
To Find :-
- What are the numbers.
Solution :-
Let, the consecutive number be x
Then,
★ First number = x
★ Second number = x + 2
According to the question,
⇒ (x + 2)² - (x)² = 36
⇒ (x + 2 + x)(x + 2 - x) = 36 [ a² - b² = (a + b)(a - b) ]
⇒ (2x + 2)(2) = 36
⇒ 4x + 4 = 36
⇒ 4x = 36 - 4
⇒ 4x = 32
⇒ x = 32/4
➠ x = 8
Hence, the required numbers are :
★ First number :
⇒ x
➲ 8
★ Second number :
⇒ x + 2
⇒ 8 + 2
➲ 10
∴ The numbers are 8 and 10.
__________________________
Question No 4 :-
➦ The difference between the squares of two consecutive odd numbers is 56. Find the numbers.
Given :-
- The difference between the squares of two consecutive odd numbers is 56.
To Find :-
- What are the numbers.
Solution :-
Let, the consecutive number be x
Then,
★ First number = x
★ Second number = x + 2
According to the question,
⇒ (x + 2)² - (x)² = 56
⇒ (x + 2 + x)(x + 2 - x) = 56 [ a² - b² = (a + b)(a - b) ]
⇒ (2x + 2)(2) = 56
⇒ 4x + 4 = 56
⇒ 4x = 56 - 4
⇒ 4x = 52
⇒ x = 52/4
➠ x = 13
Hence, the required numbers are :
★ First number :
⇒ x
➲ 13
★ Second number :
⇒ x + 2
⇒ 13 + 2
➲ 15
∴ The numbers are 13 and 15.
__________________________
Question No 5 :-
➦ The sum of two numbers is 90. One-third of the larger number is 9 more than twice the smaller one. What are the numbers.
Given :-
- The sum of two numbers is 90. One-third of the larger number is 9 more than twice the smaller one.
To Find :-
- What are the numbers.
Solution :-
Let,
★ Smaller number = x
★ Larger number = 90 - x
According to the question,
⇒ 1/3 (90 - x) = 9 + 2x
⇒ (90 - x) = 3(9 + 2x)
⇒ (90 - x) = 27 + 6x
⇒ 90 - x = 27 + 6x
⇒ 90 - 27 = 6x + x
⇒ 63 = 7x
⇒ 63/7 = x
⇒ 9 = x
➠ x = 9
Hence, the required numbers are :
★ Smaller number :
⇒ x
➲ 9
★ Larger number :
⇒ 90 - x
⇒ 90 - 9
➲ 81
∴ The numbers are 9 and 81.