Question

Penny is a dentist. She took a survey of her patients to see which type of toothbrush they prefer. Her 50 male patients prefer electric toothbrushes to manual ones in a 3:2 ratio. Her 65 female patients prefer electric to manual in a 8:5 ratio. In all, her patients prefer electric toothbrushes to manual ones in what ratio?

Answer 1

male = 30 + 20 = 50
female = 40 + 25 = 65
total = 70 + 45 = 115
so total electric:manual ratio is 70:45

Where do those numbers come from?
3:2 ratio is 5. 3/5 electric; 2/5 manual.
Percent like = (3/5)*100 = 60% electric
(2/5)*100 = 40% manual
Then 0.6*50 total = 30 electric
and 0.4*50 = 20 manual

female total = 65
ratio is 8:5 or 8/13 electric and 5/13 manual.
percent electric = (8/13)*100 = about 61%.
percent manual = (5/13)*100 = about 39%
Total is 65 so
0.61 x 115 = 40 electric
0.39 x 115 = 25 manual

male = 30 + 20 = 50
female = 40 + 25 = 65
total = 70 + 45

ratio of elec/man is 70:45