One number is 12 more than another. The sum of the smaller number and twice the larger number is 39. Find the larger number.
This is what I have so far:
x+y+12=39
You just have an extra variable.
x = the smaller number
x + 12 = the larger number
Now, write the equation according to the sentence "the sum of the..." and solve.
This is how I worked it:
n+12=m
n=m+12
m=5
m=17
I don't see how you got the answer from that, unless you guessed and checked. Your answers are correct by plugging them into the sentence.
I would have written this equation and then solved:
x + 2(x+12) = 39
To solve this problem, you can set up a system of equations. Let's call the smaller number x and the larger number y.
Given the information, we can write the following equations:
1) "One number is 12 more than another":
y = x + 12
2) "The sum of the smaller number and twice the larger number is 39":
x + 2y = 39
Now, we have a system of two equations. We can solve this system by substitution or elimination.
Let's use substitution. Rearrange equation 1) to solve for x in terms of y:
x = y - 12
Now substitute this expression for x in equation 2):
(y - 12) + 2y = 39
3y - 12 = 39
3y = 39 + 12
3y = 51
y = 17
So, the larger number is y = 17.