For every 7 candy bars that Emma sells, Robert sells 2. They sold 81 candy bars altogether last week. How many fewer candy bars did Robert sell than Emma?
E = Emma's candy bars
R = Robert's candy bars
For every 7 candy bars that Emma sells, Robert sells 2 means:
E / R = 7 / 2
Cross multiply
2 E = 7 R
Divide both sides by 2
E = 7 / 2 R
They sold 81 candy bars altogether last week means:
E + R = 81
Replace E with 7 / 2 R in this equation
7 / 2 R + R = 81
7 / 2 R + 2 / 2 R = 81
9 / 2 R = 81
Multiply both sides by 2
9 R = 162
Divide both sides by 9
R = 162 / 9 = 18
Robert sells 18 candy bars
E = 7 / 2 R
E = 7 / 2 • 18 = 126 / 2 = 63
Emma sells 63 candy bars
E - R = 63 - 18 = 45
Robert sell 45 fewer candy bars than Emma