the sum of three numbers is 60. One number is ten more than a second number. It is also twice the third. Find the numbers.
The three numbers are
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what is twice a certain number is 44. What is the number abeka. 7th grade.
To solve this problem, we can assign variables and create equations based on the given information.
Let's assume:
First number = x
Second number = y
Third number = z
From the given information, we have three conditions:
1) The sum of the three numbers is 60:
x + y + z = 60
2) One number is ten more than the second number:
x = y + 10
3) One number is twice the third number:
x = 2z
Now we can solve the equations to find the values of x, y, and z.
To start, we can substitute the value of x from equation 3 into equation 2:
2z = y + 10
Now, let's simplify this equation:
y = 2z - 10
Next, we substitute the values of x and y from equations 2 and 3 into equation 1:
(y + 10) + y + z = 60
Simplifying this equation:
2y + z = 50
Now we have a system of two equations with two variables (y and z). We can use these equations to solve for y and z.
From equation 2:
y = 2z - 10
Substituting this into equation 1:
2(2z - 10) + z = 50
Simplifying:
4z - 20 + z = 50
5z - 20 = 50
5z = 70
z = 14
Now that we have the value of z, we can substitute it back into equation 2 to find y:
y = 2(14) - 10
y = 28 - 10
y = 18
Finally, substituting y and z into equation 1 gives us the value of x:
x + 18 + 14 = 60
x + 32 = 60
x = 60 - 32
x = 28
Therefore, the three numbers are x = 28, y = 18, and z = 14.
Let n = first number, n-10 the second, 3n the third.
n + (n-10) + 3n = 60
Solve for n.