question
One number is 12 more than another. The sum of the smaller number and twice the larger number is 39. Find the larger number.
You should set up some formulas using x and y, x being the smaller number and y being the larger.
N-12=M
M+2N=39
Try that M is larger number.
Thanks
To solve this problem, let's break it down step by step.
Step 1: Assign variables
Let's use "x" to represent the smaller number and "y" to represent the larger number.
Step 2: Set up equations based on the given information
"One number is 12 more than another" implies that y = x + 12.
"The sum of the smaller number and twice the larger number is 39" can be expressed as x + 2y = 39.
Step 3: Substitute the value of y from the first equation into the second equation
As we found that y = x + 12 from the first equation, we can substitute this value into the second equation:
x + 2(x + 12) = 39.
Step 4: Solve the equation
Simplifying the equation:
x + 2x + 24 = 39,
3x + 24 = 39,
3x = 39 - 24,
3x = 15,
x = 5.
Step 5: Find the larger number
Using the value of x, we can find the larger number:
y = x + 12 = 5 + 12 = 17.
Therefore, the larger number is 17.