guys please answer these questions
1. the deffence between two numbers is 8.If 2is added to the bigger number the result will be three times the smaller number. Find the numbers.
2. what are those two numbers whose sum is 58 and deffence is
3. the sum of three consecutive multiples of 7 is 777. find these multiples.
(Hint: three consecutive multiples of 7 are 'x','x+7',x+14')
Answers
Answer:
Let the two numbers be xand y, x being the greater one
Then according to the question,
x−y=8 ....(1) and x+12=3y ..(2)
From ..(2),
x=3y−12
Putting this in the ...(1)
3y−12−y=8
2y=12+8=20
y=10
From ...(1)
x−10=8
x=18
Therefore the numbers are 18 and 10
question 1:-
x=larger number
y=smaller number
x-y=8
x=y+8 Use this to substitute for x.
x+2=3y Substitute for x from above.
(y+8)+2=3y
y+10=3y Subtract y from each side.
10=2y Divide each side by 2.
5=y
x= y+8= 5+8 =13
the smaller number is 5.
The larger number is 13.
question 2:-
Let the two numbers be x and y
then according to the question,
x+y=58 and x−y=28
Adding the above two equations
x+y+x−y=58+28
2x=86
x=43
Putting the value of x in any of the equations
43+y=58
y=58=43=15
Therefore the numbers are 44 and 15
question 3:-
As given,the three consecutive multiples of 7 will be of the form:
x,x+7 and x+14
Then according to the question,
x+x+7+x+14=777
3x+21=777
3x=756
x= 756/3
x =252
x+7 = 259
x+14= 266
Multiples are 252,259,266