The sum of two numbers is 90. if 20 is added to 3 times the smaller number, the result exceeds twice the larger by 50. find the number.

X+y=90
x=smaller number
y=larger number
2y+50= 20+3x (if 20 is added to 3 times the smaller number, the result exceeds twice the larger by 50. find the number.)
x=90-y (isolate x, so you can substitute)
2y+50=20+3(90-y) - (substitution)
2y+50=20+270-3y   ( distributive property)
5y+50=20+270 ( add 3y to both sides)
5y+50=290 ( added 20+270)
5y=240 ( subtract 50 from both sides)
y=48 ( divide both sides by 5)