The sum of two numbers is 74. If the larger number is subtracted from three times the smaller, the result is 42. Find the numbers.
x + y = 74
3y - x = 42
x = 74 - y
3y - 74 - y = 42
2y = 116
y = 58
a + b = 74 so b = 74-a
3a - b = 42
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3 a - 74 + a = 42
4 a = 116
etc
-74+y not -74-y I think
To solve this problem, let's assume that the smaller number is represented by "x" and the larger number by "y".
Given that the sum of two numbers is 74, we can write the equation:
x + y = 74 - Equation 1
Also, the problem states that if the larger number is subtracted from three times the smaller, the result is 42:
3x - y = 42 - Equation 2
To find the values of x and y, we can solve this system of equations.
Method 1:
From Equation 1, we can isolate x:
x = 74 - y
Now substitute this value of x into Equation 2:
3(74-y) - y = 42
222 - 3y - y = 42
222 - 4y = 42
Next, let's isolate the variable y by moving the constant term to the other side:
222 - 42 = 4y
180 = 4y
Divide both sides by 4 to solve for y:
180/4 = 4y/4
45 = y
Substitute the value of y back into Equation 1 to find x:
x + 45 = 74
x = 74 - 45
x = 29
Therefore, the two numbers are x = 29 and y = 45.
Method 2:
You can also use the method of substitution to solve the system of equations.
Start by isolating x in Equation 1:
x = 74 - y
Substitute this expression for x in Equation 2:
3(74 - y) - y = 42
222 - 3y - y = 42
222 - 4y = 42
Move the constant term to the other side:
222 - 42 = 4y
180 = 4y
Divide both sides by 4 to solve for y:
180/4 = 4y/4
45 = y
Now substitute the value of y back into Equation 1 to find x:
x + 45 = 74
x = 74 - 45
x = 29
So, the two numbers are x = 29 and y = 45.