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)