The sum of two numbers is 25. Twice the second plus 4 is equal to the first. Find the numbers.
The difference of two numbers is 42. Thrice the first 4 more than the second. Find the numbers.
x and (25-x)
2(25-x) + 4 = x
50 - 2x + 4 = x
3 x = 54
x = 18
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x and (x+42)
3 x - 4 = x+42
2 x = 46
x = 23
2and2differnce is 5
Is 1 38/61 irrational.
the sum of two numbers is 30. The second number is 2 more than thrice the first number. Find the numbers
To solve these problems, we can set up a system of equations and solve them simultaneously. Let's solve each individually.
1) The sum of two numbers is 25.
Let's call the first number x and the second number y.
Based on the given information, we can set up two equations:
x + y = 25 (equation 1)
2y + 4 = x (equation 2)
To solve this system of equations, we will use the substitution method. We'll solve equation 2 for x and substitute it into equation 1.
First, solve equation 2 for x:
x = 2y + 4
Now substitute this expression of x into equation 1:
(2y + 4) + y = 25
Combine like terms:
3y + 4 = 25
Subtract 4 from both sides:
3y = 21
Divide both sides by 3:
y = 7
Now substitute the value of y back into equation 1 to solve for x:
x + 7 = 25
x = 25 - 7 = 18
Therefore, the two numbers are x = 18 and y = 7.
2) The difference of two numbers is 42.
Again, let's call the first number x and the second number y.
Based on the given information, we can set up two equations:
x - y = 42 (equation 1)
3x = y + 4 (equation 2)
Let's solve this system of equations using the substitution method. We'll solve equation 1 for x and substitute it into equation 2.
First, solve equation 1 for x:
x = y + 42
Now substitute this expression of x into equation 2:
3(y + 42) = y + 4
Distribute 3 to both terms within the parentheses:
3y + 126 = y + 4
Subtract y from both sides:
2y + 126 = 4
Subtract 126 from both sides:
2y = -122
Divide both sides by 2:
y = -61
Now substitute the value of y back into equation 1 to solve for x:
x - (-61) = 42
x + 61 = 42
x = 42 - 61 = -19
Therefore, the two numbers are x = -19 and y = -61.