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# Math

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1/5 of Andrew's money was \$12 more than 1/3 of Drake's money. When Andrew have Drake \$50, both of them had the same amount of money in the end. How much did Andrew have at first?

Apr 20, 2021

#1
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1/5 of Andrew' money = 1/3 of Drake's money + \$12

3/5 of Andrew's money = 3/3 of Drake's money + \$36

Difference at first --> 2/5 of Andrew's money + \$36

Difference at first --> \$50 * 2

= \$100

2/5 of Andrew's money + \$36 = \$100

\$100 - \$36 = \$64

2/5 of Andrew's money = \$64

1/5 of Andrew's money = \$32

Andrew's money = \$32 * 5

= \$160

Apr 20, 2021
#2
+1

(1/5)A  - 12   =  (1/3)D      multiply through  by  3

(3/5)A  - 36  =  D       (1)

A  - 50  =  D  + 50     (2)

Sub (1)  into  (2)  for D

A - 50 =  (3/5)A -  36 + 50

A - (3/5)A  =  - 36  + 50 + 50

(2/5)A  = 64

A = 64 (5/2)  =  160  (dollars)  = what  Andrew  started with

Proof

(1/5)A  - 12  = (1/3) D

(1/5)A   -12 =  (1/3)((3/5)A  - 36 ]

32  - 12  =   (1/3) ( 96 - 36]

20  =  (1/3) 60

20   = 20   Apr 20, 2021