A board 109 cm long has to be cut into two pieces so that the longer part is 10 cm more than twice as long as the shorter part. Find the length of each part

x = longer section

y = shorter section

x + y = 109

x = 2y + 10

so we sub in eq 2 into eq 1

2y + 10 + y = 109

3y + 10 = 109

3y = 109 - 10

3y = 99

y = 99/3

y = 33 < = = = shorter section is 33 cm

x = 2y + 10

x = 2 (33) + 10

x = 66 + 10

x = 76 < = = = longer section is 76 cm