Question
The product of two natural numbers is 18. If one is added to four times the smaller number this is equal to the larger number. Find both numbers
Answers
PsyDAG
(4 * 2) +1 = 9
Bosnian
a = the smaller number
b = the larger number
The product of two natural numbers is 18.
This mean :
a * b = 18
If one is added to four times the smaller number this is equal to the larger number.
This mean :
1 + 4 a = b
So :
b = 1 + 4 a
Replace this value in expression :
a * b = 18
a * ( 1 + 4 a ) = 18
a + 4 a ^ 2 = 18
4 a ^ 2 + a = 18 Subtract 18 to both sides
4 a ^ 2 + a - 18 = 18 - 18
4 a ^ 2 + a - 18 = 0
The solutions are : a = - 9 / 4 and a = 2
- 9 / 4 isn't the natural number.
Solution: a = 2
b = 1 + 4 a = 1 + 4 * 2 = 1 + 8 = 9
The smaller number = 2
The larger number = 9
b = the larger number
The product of two natural numbers is 18.
This mean :
a * b = 18
If one is added to four times the smaller number this is equal to the larger number.
This mean :
1 + 4 a = b
So :
b = 1 + 4 a
Replace this value in expression :
a * b = 18
a * ( 1 + 4 a ) = 18
a + 4 a ^ 2 = 18
4 a ^ 2 + a = 18 Subtract 18 to both sides
4 a ^ 2 + a - 18 = 18 - 18
4 a ^ 2 + a - 18 = 0
The solutions are : a = - 9 / 4 and a = 2
- 9 / 4 isn't the natural number.
Solution: a = 2
b = 1 + 4 a = 1 + 4 * 2 = 1 + 8 = 9
The smaller number = 2
The larger number = 9