The+sum+of+two+numbers+is+30+six+less+than+twice+the+smaller+number+is+equal+to+the+number+x+find+the+larger+number
Please give me the answer
The denominator of a fraction exceedsby 3. If the numerator is decreased by 1 and the denominator is increased by 3, the value of the resulting fraction is 1/2. What is the denominator and numerator?
Please give me the answer in detail form thanks
What's with all the + signs in the first post?
smaller ---- x
larger ----- 30-x
2x - 6 = 30-x
3x = 36
x=12
smaller is 12, larger is 30-x or 18
2nd:
I will assume you meant to type:
"The denominator of a fraction exceeds the numerator by 3"
so the original fraction is x/(x+3)
stated scenario:
(x-1)/x = 1/2
2x-2 = x
x = 2
the original numerator is 2, and the denominator is 5
that is, the fraction was 2/5
Sure, I can help you with that. Let's solve the problem step by step.
Let's denote the two numbers as "x" (the smaller number) and "y" (the larger number).
According to the problem, the sum of the two numbers is 30. So we can write the equation:
x + y = 30
The problem also states that six less than twice the smaller number is equal to the number x. Mathematically, we can write this as:
2x - 6 = x
To find the larger number, we need to solve these two equations simultaneously.
First, let's simplify the second equation by moving the variables to one side:
2x - x = 6
This simplifies to:
x = 6
Now we can substitute this value of x into the first equation to find the value of y:
6 + y = 30
Subtracting 6 from both sides, we get:
y = 30 - 6
Simplifying further, we find:
y = 24
Therefore, the larger number y is 24.
So, the solution to the problem is that the larger number is 24.