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Dean and Patrick brought some money for shopping. The ratio of the amount of money

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Dean and Patrick brought some money for shopping. The ratio of the amount of money Dean had to the amount of amount Patrick had was 3:8. The ratio of the amount of money Dean spent to the amount of money Patrick spent was 3:5. Dean spent 3/4 of his money and Patrick had \$136 left. What was the total amount of money they brought for shopping?

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D==Dean's money,  P==Patrick's money

d==How much Dean spent,  p==How much Patrick spent

D/P == 3/8..................... (1)

d/p==3/5........................ (2)

D - d ==1/4D.................. (3)

P - p==136..................... (4), solve for D, P, d, p

From (1) and (2) above, we have:

d==0.60p   and  D==0.375P        (5)

Sub d  and  D in (3) above and we have:

0.375P - 0.60p ==1/4 * 0.375P

P - p == 136, solve for P, p

P==\$256 - Patrick's money

p==\$120 - what Patrick spent

Sub P and p into (5) above:

D==0.375 * 256==\$96 Deans money

d==0.60 * 120==\$72 - what Dean spent.

Sep 4, 2023