[tex]\large{ \pink{DIRECTION:}}[/tex]
Find two consecutive numbers such that 4 more than half of their product is 70
[tex]\large{ \pink{ANSWER:}}[/tex]
Step-by-step explanation:
Let x be the number
- 1st number = x
- 2nd number = x+1
So, 4 more than half their product is
- [ (x)(x+1) / 2 ] + 4 = 70
solving for x
- [ (x)(x+1) / 2 ] + 4 = 70
- [ (x²+x) / 2] + 4 = 70
- (x²+x)/2 = 70 - 4
- (x²+x)/2 = 66
- x²+x = 66×2
- x²+x = 132
- x²+x-132 = 0
Then solve for the positive root
- x²+x-132 = 0
- (x-11)(x+12) = 0
The positive root is
Lastly, we will substitute the value of x to the second integer
- 1st integer = x = 11
- 2nd integer = x+1 = 11+1 = 12
Therefore, the 2 consecutive numbers are 11 and 12
