The sum of three numbers is 147. The second number is 4 more than two times the first number. The third number is five less than three times the first number. Find the three numbers.
Can you please solve it? I have no idea how to do this. Thanks a lot for any help!
Call the numbers A, B and C
We know
A + B + C = 147
We are told that:
B = 2 A + 4 (two times the first number and add 4)
and
C = 3 A - 5 (five less than three times the first number)
This is called substituting. Now we can substitute (2 A + 4) for B whenever we see it.
Using this, we can rewrite
A + B + C = 147
as
A + (2 A + 4) + (3 A - 5) = 147
since we know B and C in terms of A.
Make sure you understand this step before continuing.
Gathering the As and the numbers together, we have:
A + 2A + 3A + 4 - 5 = 147
6 A + 4 - 5 = 147.
6 A - 1 = 147.
6 A = 148.
A = 148 / 6.
A = 24 2/3
B = 2 A + 4 = 49 + 4 + 1/3 = 53 1/3
C = 74 - 5 = 69.
i think the answeris letter c
To solve this problem, let's assign variables to each of the numbers. Let's call the first number "x", the second number "y", and the third number "z".
We are given three pieces of information:
1. The sum of the three numbers is 147.
This can be written as an equation: x + y + z = 147.
2. The second number is 4 more than two times the first number.
This can be represented as: y = 2x + 4.
3. The third number is five less than three times the first number.
This can be represented as: z = 3x - 5.
Now, we have a system of three equations:
Equation 1: x + y + z = 147
Equation 2: y = 2x + 4
Equation 3: z = 3x - 5
We can solve this system by substituting Equation 2 and Equation 3 into Equation 1.
From Equation 2, we can solve for y: y = 2x + 4.
Now, substitute this value of y into Equation 1:
x + (2x + 4) + z = 147
3x + z + 4 = 147
Rearrange the equation to isolate z:
z = 147 - 3x - 4
z = 143 - 3x
Now, substitute this value of z into Equation 1:
x + (2x + 4) + (143 - 3x) = 147
3x + 147 - 3x + 4 = 147
Combine like terms:
7x + 151 = 147
Subtract 151 from both sides:
7x = -4
Divide by 7:
x = -4/7
Now we have the value of x. We can substitute it back into Equation 2 and Equation 3 to find y and z:
From Equation 2: y = 2x + 4
Substitute x = -4/7:
y = 2(-4/7) + 4
y = -8/7 + 4
y = -8/7 + 28/7
y = 20/7
From Equation 3: z = 3x - 5
Substitute x = -4/7:
z = 3(-4/7) - 5
z = -12/7 - 35/7
z = -47/7
So, the three numbers are x = -4/7, y = 20/7, and z = -47/7.
Let the first number be x
"The second number is 4 more than two times the first number"
the second number is 2x + 4
"The third number is five less than three times the first number"
the third number is 3x - 5
your first sentence "The Sum of three numbers is 147"
x + 2x+4 + 3x-5 = 147
6x = 148
x = 74/3
then second number is 2(74/3) + 4 = 160/3
the third number is 3(74/3) - 5 = 39
check: 74/3 + 160/3 + 69 = 147