The sum of two numbers is 43. The smaller number is 15 less than the larger number. What are the numbers
x + x+15 = 43
2 x = 28
x = 14
x+15 = 29
Let x = larger number
x + x - 15 = 43
Let's assume the smaller number is x and the larger number is y.
According to the given information:
1. The sum of two numbers is 43:
x + y = 43 (Equation 1)
2. The smaller number is 15 less than the larger number:
x = y - 15 (Equation 2)
To find the values of x and y, we can solve this system of equations.
Substituting Equation 2 into Equation 1:
(y - 15) + y = 43
Simplifying the equation:
2y - 15 = 43
Adding 15 to both sides of the equation:
2y = 43 + 15
2y = 58
Dividing both sides by 2:
y = 58 / 2
y = 29
Now, substituting the value of y back into Equation 2:
x = 29 - 15
x = 14
So, the smaller number is 14 and the larger number is 29.
To find the numbers, we can set up a system of equations based on the given information.
Let's assume the larger number is 'x' and the smaller number is 'y'.
From the first statement, we know that the sum of two numbers is 43. So, we can write the equation:
x + y = 43 (Equation 1)
From the second statement, we know that the smaller number is 15 less than the larger number. Mathematically, this can be expressed as:
y = x - 15 (Equation 2)
Now, we have a system of equations with Equation 1 and Equation 2. We can solve this system of equations to find the values of x and y.
To do this, we can use the substitution method or the elimination method. Let's use the substitution method in this case.
Step 1: Substitute Equation 2 (y = x - 15) into Equation 1.
x + (x - 15) = 43
Step 2: Simplify the equation.
2x - 15 = 43
Step 3: Add 15 to both sides of the equation.
2x = 43 + 15
2x = 58
Step 4: Divide both sides of the equation by 2.
x = 58 รท 2
x = 29
So, we have found that the larger number (x) is 29.
Step 5: Substitute the value of x (29) into Equation 2 to find y.
y = 29 - 15
y = 14
Therefore, the smaller number (y) is 14.
In conclusion, the larger number is 29 and the smaller number is 14.