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# Math

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2/5 of Elvis's money was 6/7 of Noah's money. After Noah received \$20 from his mother and Elvis spent \$36 on a bag, both of them had an equal amount of money left. How much did Elvis have in the end?

Apr 24, 2021

#1
+1

Lets say E is Elvis's money and N is Noah's Money
Start by making an equation:
2/5•E=6/7•N
And make a second equation:
N+20 = E - 36
N + 56= E
You can derive this from the second sentence.
Then plug in N+56=E into the first equation:
2/5(N+56)=6/7 N
Multiply by 35 on both sides to cancel the denominators
14(N+56) = 30 N
14 N + 14 • 56 = 30 N
14 • 56 = 16 N
Divide both sides by power of 2 till N is isolated so the calculation isn't so messy.
14 • 7 = 2 N
7 • 7 = N
49 = N
We need to find elvis's money at the end
That is equal to 49+20 = 69

Apr 24, 2021
#2
+1

(2/5)E  =  (6/7)N

(7/6) (2/5)E  =  N

(14/30)E  =  (7/15)E   = N

E - 36  =  N  + 20

E - 36  =  (7/15)E  +  20

E  -  (7/15)E  =  20  +  36

(8/15)E   =   56

E  =  (15/8)(56)

E  =  15  ( 56/8)

E  =  105   =   what  he started with

So.....he  ended  up  with    105 - 36  =   \$69   Apr 24, 2021