the ratio of two number is 2:3 and their sum is 30 find the numbers
let the number be
a:b=2:3
a+b=30
now
a/b=2/3
a=2b/3
input above
2b/3+b=30
2b+3b=90
5b=90
b=18
i live to to find the other value now
a / b = 2 / 3 Multiply both sides by b
a = ( 2 / 3 ) b
a + b = 30
( 2 / 3 ) b + b = 30
( 2 / 3 ) b + ( 3 / 3 ) b = 30
( 5 / 3 ) b = 30 Multiply both sides by 3
5 b = 30 * 3
5 b = 90 Divide both sides by 5
b = 90 / 5 = 18
a = ( 2 / 3 ) b = 2 * 18 / 3 = 36 / 3 = 12
a / b = 12 / 18 = ( 2 * 6 ) / ( 3 * 6 ) = 2 / 3
2+3=5
sum=30
first number=2/5*30=12
second number=3/5*30=18
verify:
12+18=30
To find the two numbers, let's assign variables to them.
Let's say the first number is "x" and the second number is "y."
According to the given information, the ratio of these two numbers is 2:3. In other words,
x/y = 2/3
Next, we know that the sum of these two numbers is 30. So we can write an equation based on this:
x + y = 30
Now we have a system of two equations:
1) x/y = 2/3
2) x + y = 30
To solve this system, we can use substitution or elimination method. Let's use the substitution method here.
From equation 1), we can solve for x in terms of y:
x = (2/3)y
Now, substitute this value of x into equation 2):
(2/3)y + y = 30
Multiply through by 3 to eliminate the fraction:
2y + 3y = 90
Combine like terms:
5y = 90
Divide both sides by 5:
y = 18
Now, substitute this value of y back into either of the original equations to find x:
x = (2/3)(18)
x = 12
Therefore, the two numbers are 12 and 18.