SOLUTION: Alpha has £160 more than beta. After giving1/10 of his money to Beta, Alpha has three times as much money as Beta. How much money do they each have to start with?

Question 1136842: Alpha has £160 more than beta. After giving1/10 of his money to Beta, Alpha has three times as much money as Beta. How much money do they each have to start with?
Answer by ikleyn(52847) (Show Source): You can put this solution on YOUR website!
.


a = b + 160                 (1)

a - 0.1a = 3*(b + 0.1a)     (2)



Equation (2) is equivalent to

0.9a = 3b + 0.3a      or

0.9a - 0.3a = 3b,

0.6a = 3b                   (3)



From eq(1), substitute a = b+160 into eq(3).



0.6*(b+160) = 3b


0.6*b + 0.6*160 = 3b

0.6*160 = 3b - 0.6b

96           = 2.4*b


b            =  = 40.


ANSWER.  Beta started with £40;  Alpha started with  £40 + £160 = £200.


CHECK.   200 - 20 = 180;  40 + 20 = 60.   180 is three times 60.   ! Correct !

Solved.

RELATED QUESTIONS
Alpha and Beta each have a collection of marbles. At first,Beta has 2/5as many marbles as (answered by josmiceli)

Rewrite the expression as a simplified expression containing one term: cos (alpha +... (answered by jsmallt9)

Prove that sin(alpha+beta)= sin alpha cos beta+cos alpha sin beta I have no idea how... (answered by richard1234)

Hi, i'm just not sure how to even start this problem? Thanks for the help! Given... (answered by stanbon)

Establish the identity sin (alpha + beta)/(cos alpha cos beta) = tan alpha + tan... (answered by Edwin McCravy)

Verify the identity Tan (alpha sign)+ cot( beta)= tan(beta)+cot(alpha)/tan(beta) cot... (answered by math_tutor2020)

Find the Exact value (No Decimals) of sin(105 degrees) using the sum or difference... (answered by Theo)

Solve Problems Using Linear Systems 2. James looks in his TV cabinet and finds some old... (answered by scott8148)

Verify that each equation is an identity.... (answered by jsmallt9)