the sum of 2 numbers is 45 and one of them is 13 more than the other. find the numbers
Answers
Answer:
The numbers are 16 and 29.
Step-by-step explanation:
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✯ ᴀɴsᴡᴇʀ ✯
★ given →
☞︎︎︎ ・sum of 2 numbers is 45 and one
・number is 13 more than the other
★ to find →
☞︎︎︎ find the numbers?
★ solution →
☆ first way →(linear equation in one variable)
☞︎︎︎ let a number be x
and according to question( one number is 13 more than the other)
then, other number is x + 13
we have sum of two numbers is 45
➪ x + ( x+ 13 ) = 45
➪ x + x + 13 = 45
➪ 2x = 45 - 13
➪ 2x = 32
➪ x = 32/2
➪ x = 16
so, one number is 16
then, other number is x + 13
→ 16 + 13 = 29
hence, the numbers are 16 and 29 ✔︎
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☆ second way → ( Linear equation in two variables)
☞︎︎︎ let a number be x and other number be y
and we have sum of numbers is 45
➪ x + y = 45
➪ x + y - 45 = 0 ............(i)
and according to question ( a number is 13 more than other number )
➪ x = y + 13
➪ x - y - 13 = 0 ................(ii)
now we have two linear equations:
・ x + y - 45 = 0 .............(i)
・ x - y - 13 = 0 ...............(ii)
now solve these equations by elimination method!
adding equations (i) and (ii) , we get
➪ x + y - 45 + ( x - y - 13 ) = 0
➪ x + y - 45 + x - y - 13 = 0
➪ x + x + y - y - 45 - 13 = 0
➪ 2x - 58 = 0
➪ 2x = 58
➪ x = 58/2
➪ x = 29
now substitute the value of x in eq.(i)
x + y - 45 = 0
➪ 29 + y - 45 = 0
➪ y - 16 = 0
➪ y = 16
since, value of x is 29 and value of y is 16
so that, two Numbers are 16 and 29
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★ verification ✍︎
☞︎︎︎ sum of numbers = 45
→ 16 + 29 = 45
→ 45 = 45
LHS = RHS
☞︎︎︎ a number is 13 more than other
→ 29 = 16 + 13
→ 29 = 29
LHS = RHS