The sum of two numbers is 184 one third of one number exceeds one seventh of the other other number by 8
Answers
let one number = x
second number = 184 - x
according to the problem given,
x /3 - ( 184 -x )/7 = 8
[ 7x - 3(184 - x ) ] /21 = 8
7x - 552 + 3x = 21 × 8
10x = 168 + 552
10x = 720
x = 720 / 10
x = 72
Therefore ,
one number = x = 72
second number = 184 - x
= 184 - 72
=12
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Step-by-step explanation:
☆ Given:
● Sum of two numbers = 184. So let the numbers be x and y.
● 1/3 of 1st number exceeds 1/7 of 2nd number by 8. So, 1/3x - 8 = 1/7y
We will use these two given information to form two equations.
1. x + y = 184
2. 1/3x - 8 = 1/7y
= 1/3x - 1/7y = 8
Now, we will solve these two equations as simultaneous linear in equation.
• x + y = 184
• 1/3x - 1/7y = 8
we will multiply equation (2) by 3 to cancel out the variable x
x + y = 184
(1/3x - 1/7y = 8) × 3
=) x + y = 184
=) x - 3/7y = 24
3/7y + y = -24 + 184
= 3y + 7y/7 = 160 ( taking 7 as l.c.m)
= 10y = 160 × 7
= 10y = 1120
= y = 1120/ 10
= y = 112
Now, putting the value of y in eq 1 we will get the value of x
x + 112 = 184
x = 184 -112
x = 72
So, 1st number is 72 and 2nd number is 112
☆Cross checking
■ Sum of x and y = 184
72 + 112 = 184
verified
■ 1/3x - 1/7y = 8
1/3x = 1/3× 72
= 24 (1)
1/7y = 1/7 × 112
= 16 (2)
=) 24 - 16 =8
Hence, verified.