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# Math

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Andy and Bruce had some money. Andy had 50% more money than Bruce. After Andy gave Bruce \$77, Bruce had 25% more money than Andy.
(a) How much money did they have in total?

(b) How much money must Bruce then give to Andy so that Andy wouldl have 50% more money than Bruce?

Jun 11, 2022

#1
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(a) According to the information,

x = 1.5y (1)

y + 77 = 1.25 (x - 77) (2)

x = 297, y = 198

x + y = 297 + 198 = \$495

They have \$495 in total.

(b)        Let the money that Bruce then give to Andy be a.

After Andy gave Bruce \$77, Andy had 297 - 77 = \$220

Bruce had 198 + 77 = \$275

220 + a = 1.5 (275 - a)

a = 77

Bruce must give Andy \$77 so that Andy would have 50%

more money than Bruce

Jun 11, 2022
#2
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And we  know that

(1.5B - 77) *1.25  =  B + 77         simplify

1.875B  - 96.25 = B + 77

1.875B - B  = 77 + 96.25

.875B  = 173.25

B =  173.25  / . 875  =  \$198  =  what Bruce started wih

1.5 B  = \$297  = what Andy started with

a)  They had    198 + 297 =  \$495  in  total

b)   If Bruce returns the \$77 to Andy....the original  relationship still holds....Andy has 50% more money than Bruce   Jun 11, 2022