Pei had 5/8 as much money as Jason. Pei gave Jason $36. As a result Pei now has 1/5 of the total sum of money they have altogether. How much had Pei in the beginning?
Pei had 5/8 as much money as Jason. Pei gave Jason $36. As a result Pei now has 1/5 of the total sum of money they have altogether. How much had Pei in the beginning?
Jason had =J amount of money
Pei had 5/8J as much money
5/8J - 36=1/5(J +5/8J - 36)
Jason had =$96
Pei had 5/8 X 96=$60
Solve for J:
(5 J)/8-36 = ((13 J)/(8)-36)/(5)
Put each term in (13 J)/(8)-36 over the common denominator 8: (13 J)/(8)-36 = (13 J)/8-(288)/8:
(5 J)/8-36 = ((13 J)/8-(288)/8)/(5)
(13 J)/8-(288)/8 = (13 J-288)/8:
(5 J)/8-36 = ((13 J-288)/8)/(5)
Put each term in (5 J)/8-36 over the common denominator 8: (5 J)/8-36 = (5 J)/8-(288)/8:
(5 J)/8-(288)/8 = (13 J-288)/(8×5)
(5 J)/8-(288)/8 = (5 J-288)/8:
(5 J-288)/8 = (13 J-288)/(8×5)
Multiply both sides by 8:
5 J-288 = (13 J-288)/5
Multiply both sides by 5:
5 (5 J-288) = (5 (13 J-288))/5
(5 (13 J-288))/5 = 5/5×(13 J-288) = 13 J-288:
Answer: | 5 (5 J-288) = 13 J-288 J=96
