SOLUTION: HELP!!!! Translate to a system of equations and solve: The difference between two numbers is 16. Three times the larger number is seven times the smaller. What are the number

Algebra ->  Expressions-with-variables -> SOLUTION: HELP!!!! Translate to a system of equations and solve: The difference between two numbers is 16. Three times the larger number is seven times the smaller. What are the number      Log On


   

Question 26883: HELP!!!! Translate to a system of equations and solve:
The difference between two numbers is 16. Three times the larger number is seven times the smaller. What are the numbers?
What we've tried: a-b=16 3a=7b That's about all I've done...I'm so confused I don't know where to begin.
Thanks!
Answer by bmauger(101) About Me  (Show Source):
You can put this solution on YOUR website!
Then you've done the hard part... most people have trouble translating from english to math, but you're doing fine so far. Just need to solve the system of equations.
a-b=16
3a=7b
The easiest way for this particular problem is substitution, solving the first equation for a you get:
a=16%2Bb When you put that into equation 2...
3%2816%2Bb%29=7b
Distribute: 48%2B3b=7b
Rearrange: 48=4b
Solve: 12=b
Substituting in for equation 1:
a-12=16
a=28
Double check: 3%2A28=847%2A12=84 check.