The secound of two numbers is 6 times the first.Their sum is 77.Find the numbers.

Question

In this math problem i have to find an equation.ex. 2x+3=9. in the whole problem an wquation lies in it and i am thrown off by my answers. in this example 2x = there is 2 unknowns and 3 is the number i know just like the whole equation =9 so i just need an equation. Ill do the rest my self

Answer 1

Adrian,

 

If you look at the equation in its entirety before you try to write equations, you can find that the information "the first number" "second number" is useless. There is more, it could confuse you

 

Solution: you have two numbers and it's of no consequence which is first - just give them a name like x, y, a , b...etc 

 

Then you get to say a = 6b and a + b = 77

 

Now do substitution 6b + b = 77 => 7b = 77 => b = 11 and a = 66

Answer 2

For two unknown numbers, you'll need two equations, which you have with this information.  

 

• Label your variables, x and y for the two numbers works just fine
• y = 6x (this is your "second of two numbers is 6 times the first")
• x+y = 77 ("their sum is 77")

 

Now you need a plan to solve these equations.  The elimination method works well here, since your one equation is already in the y=something format

 

• x + 6x = 77 (plugging the y=6x equation in for y in the second equation)
• 7x=77 (combine like terms)
• x=11 (divide both sides by 7, and now you have one of the numbers)
• y=6x = 6*11 = 66 (now you have the second number)
• Your numbers are 11 and 66