the larger of two numbers is 12 mo're than the smaller.Their sum 84. Find the numbers.
If you came up with 36,48 you are correct
To find the two numbers, let's set up a system of equations based on the given information.
Let's denote the smaller number as 'x' and the larger number as 'y'.
1. We know that the larger number is 12 more than the smaller number, so we can write the equation: y = x + 12.
2. We also know that their sum is 84, so we can write the equation: x + y = 84.
Now, we have a system of two equations:
y = x + 12
x + y = 84
To solve this system, we can use the method of substitution or elimination.
Method 1: Substitution
1. Substitute the value of y from the first equation into the second equation: x + (x + 12) = 84.
2. Simplify the equation: 2x + 12 = 84.
3. Subtract 12 from both sides: 2x = 72.
4. Divide both sides by 2: x = 36.
Now substitute x = 36 into the first equation to find y:
y = 36 + 12 = 48.
So, the smaller number is 36 and the larger number is 48.
Method 2: Elimination
1. Add the two equations: (x + y) + (x + 12) = 84.
2. Simplify and combine like terms: 2x + y + 12 = 84.
3. Subtract 12 from both sides: 2x + y = 72.
Now subtract the first equation from this new equation:
(2x + y) - (x + y) = 72 - 84,
x = -12.
But we know that x represents the smaller number, so a negative value does not make sense in this context.
Therefore, we discard this solution and proceed with the solution obtained from method 1.
Hence, the smaller number is 36 and the larger number is 48.