# Thread: Correction help with this

1. ## Correction help with this

The sum of two numbers is 78. If the smaller number is 12 less than one- fifth of the larger number, find the two numbers.

Attempt 1

a + a + 12 - a/5 = 78

5a + 5a + (5)12 - (5) a/5 = 78 * 5

5a + 5a + 60 - a = 390

9a = 390 - 60

9a = 330

a = 3.66

Attempt 2

A + 12 (1/5)a = 78 :

I think the second attempt is completely wrong

2. ## Re: Correction help with this

$a+b=78$

let $a < b$

$a=\dfrac 1 5 b - 12$

$b + \dfrac 1 5 b - 12 = 78$

$\dfrac{6}{5}b = 90$

$b = 90 \cdot \dfrac{5}{6} = 75$

$a = \dfrac{75}{5}-12 = 3$

$(a,b) = (3,75)$

3. ## Re: Correction help with this

So the equation is substitution elimination ?

4. ## Re: Correction help with this

Originally Posted by diehardmath4
So the equation is substitution elimination ?
I'm sorry I don't know what that means.

I just call it algebra.

5. ## Re: Correction help with this

diehardmath4, where did you get "a + a + 12 - a/5 = 78"? What was your reasoning? I can guess that the "12- a/5" is from "twelve less than 1/5 the number" but "12 less than" something is that something minus 12, not 12 minus something. And then, I guess, "a" is the first number. But why do you have "a+ a"?