Answered

The difference between two numbers is 14.Three times the larger number is two more than 5 times the smaller. What are the numbers ?

Sagot :

Mariamikaylaviz
[tex]a-b=14 \\\\ 3a=5b+2 \\\\ \boxed{a=\frac{5b+2}{3}} \\\\\\ \frac{5b+2}{3}-b^{(3}=14^{(3} \\\\ 5b+2-3b=42 \\\\ 2b=42-2 \\\\ 2b=40 \ |:2 \\\\ \boxed{\boxed{b=20}} \\\\ a= \frac{5*20+2}{3} \\\\ a=\frac{100+2}{3} \\\\ a=\frac{102}{3} \\\\ \boxed{\boxed{a=34}}[/tex]
Jeremiaviz
First, translate it to linear equation:
Let the larger number be x and the smaller number y:
x-y=14
3x=5y+2

Transpose it and use the amazing concept of SUBSTITUTION!!
(Reminder: If something goes to the other side, its sign is changed!)
x-y=14
x-14=y
So, use x-14 as your y for the second equation!!!
3x=5y+2
3x=5(x-14) + 2
3x=5x-70+2
3x=5x-68
3x-5x=-68
-2x=-68
-2x/-2=-68/-2
x=34
x-y=14
34-y=14
34-14=y
y=20
So:
x=34 and y=20
Check:
x-y=14
34-20=14
14=14, Check!
3(34)=5(20)+2
102=100+2
102=102, Check!!
Therefore, the larger number is 34 and the smaller number is 20!