Betty and Diana have $331. Penelope and Betty have $382. The ratio of Diana to Penelope is 4 : 7. How much does Betty have?
Amount that Diana has = 4 u
Amount that Penelope has = 7 u
The amount that Betty has is the repeated identity.
Betty + 4 u = 331 --- (1)
Betty + 7 u = 382 --- (2)
(2) - (1)
7 u - 4 u = 382 - 331
3 u = 51
1 u = 51 ÷ 3 = 17
From (1):
Betty + 4 u = 331
Betty + 4 x 17 = 331
Betty + 68 = 331
Amount that Betty has
= 331 - 68
= $263
Answer(s): $263
