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

2
by TatsXD

2014-12-13T18:20:17+08:00

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
2014-12-13T19:45:50+08:00

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
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!