Three times a number minus two times another number equals 19. The sum of the two number is 18. find the two numbers
Let m = one of the numbers and n = the other number
We have two unknowns (n and m), so we need two equations relating them to find the solution.
Equation 1 - Three times a number minus two times another number equals 19
3m - 2n = 19
Equation 2 - The sum of the two numbers is 18
m + n = 18
We can re-write this equation as:
n = 18 - m
Now let's substitute 18-m in place of n in Equation 1:
3m - 2n = 19 (equation 1)
3m - 2(18-m) = 19 (Substitute 18-m in place of n)
3m - 36 +2m = 19 (Multiply out the parentheses)
5m = 55 (Add the m terms, add 36 to both sides)
Solve for m, then use n = 18 - m to solve for n. Check your answers by putting them into equation 1 and verifying that they produce 19 for the answer.
