3)The original rational number was 17/12.
4)The age of Ruby and Reshma are 20 and 28 years respectively.
Explanation:
3)Let the numerator be x.
So denominator will be (x - 5)
If we add 5 to numberator then it will be (x + 5)
New number is (x + 5)/(x - 5)=11/6
Solve for X by cross multiplying
6(x + 5)=11(x - 5)
6x + 30=11x - 55
5x=85
x=17
So original rational number was 17/12.
4)The ages of Ruby and Reshma are in the ratio 5:7
So, let the present ages of Ruby and Reshma be 5x and 7x respectively.
Also, it is given that four years from now the ratio of their ages will be 3:4
So, the equation - 5x + 4 / 7x + 3 = 3/4
⇒4(5x+4)=3(7x+4)
⇒20x+16=21x+12
⇒21x−20x=16−12
⇒x=4
⇒5x=20 and 7x=28
The age of Ruby and Reshma are 20 and 28 years respectively.
C. 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60
1,000: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000
Now we find the common numbers. One doesn’t count as when multiplied later on, it will not change anything.
60: 2, 4, 5, 10, 20
1,000: 2, 4, 5, 10, 20
The highest common factor is 20 because it’s, well, the highest number.
D. Do the same thing for D.
24: 1, 2, 3, 4, 6, 8, 12, 24
880: 1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 40, 44, 55, 80, 88, 110, 176, 220, 440, 880
20 and 880: 2, 4, 8
8 is the Highest Common Factor.
E. Do the same thing with E.
90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
1,000: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000
90 and 1000: 2, 5, 10
10 is the Highest Common Factor.
Since it says when Added they are a negative and when multiplied they are positive, we know our two numbers are negative.
think of all multiples of 24
6 and 4
8 and 3
12 and 2
24 and 1
however, none of our choices here would be correct.
