If Terry gives $100 to Aaron the ratio of their money will be 4 : 9. If Terry gives $300 to Aaron?_help_Articles

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If Terry gives $100 to Aaron the ratio of their money will be 4 : 9. If Terry gives $300 to Aaron?

... their ratio will be 2 : 11. How much does Terry have ? or:... their ratio will be 2 : 11. How much does Terry have ?or:LetT = Amount of Terry's

... their ratio will be 2 : 11. How much does Terry have ?

or:... their ratio will be 2 : 11. How much does Terry have ?

or:LetT = Amount of Terry's money,A = Amount of Aaron's moneybefore any financial transaction has taken place.1st condition: If Terry gives $100 to Aaron the ratio of their money will be 4 : 9In mathematical terms:(T - 100) / (A + 100) = 4/9 ; which gives us Equation 1 :9T - 900 = 4A + 400 2nd condition: If Terry gives $300 to Aaron the ratio will be 2 : 11(T - 300) / (A + 300) = 2/11 ; which gives us Equation 2 :11T - 3300 = 2A + 600Subtract equation 1 from equation 2:2T - 2400 = -2A + 2002T - 2600 = -2A ; divide by -2, which yields Equation 3 :A = -T + 1300 ; As we can now express A in terms of T, this is our key to isolate T:We substitute A by -T+1300 in, say, equation 1:9T - 900 = 4(-T + 1300) + 4009T - 900 = -4T +5200 +4009T - 900 = -4T + 560013T = 6500T = 500 ; here we are essentially done but in order to validate our result, ...... we insert this value for T in Equation 3:A = -500 + 1300A = 800 ; and check, wether the results fit the primary conditions:1)(500 - 100) / (800 + 100) = 400 / 900 = 4/9 ;;TRUE2)(500 - 300) / (800 + 300) = 200 / 1100 = 2/11 ;;TRUESo, Terry's got $500 and Aaron's got $800.

or:You don't say which is the top of the ratio and which is the bottom.(A + 100) / (T - 100) = 4/9(A + 300) / (T - 300) = 2/11Reducing:(A + 100) / (T - 100) = 4/9 Multiply by 9(T -100)9(A + 100) = 4(T - 100) Evaluate.9A + 900 = 4t - 400 Subtract 900.9A = 4T - 1300 Divide by 9.A = 4T/9 - 1300/9Reduce the second equation:(A + 300) / (T - 300) = 2/11 Multiply by 11(T - 300).11(A + 300) = 2(T - 300) 11A + 3300 = 2T - 600 Subtract 3300.11A = 2T - 3900 Divide by 11.A = 2T/11 - 3900/11Now you have two expressions equal to A, so just set them equal to each other.4T/9 - 1300/9 = 2T/11 - 3900/11 Multiply by 99 to get rid of fractions.44T - 14300 = 18T - 35100 Subtract 18T.26T - 14300 = -35100 Add 14300.26T = -20800 Divide by 26.T = -800 Plug this into either original equation to get A.(A + 100) / (T - 100) = 4/9(A + 100)/(-900) = 4/9A + 100 = -400A = -500Check:(A + 300) / (T - 300) = 2/11(-500 + 300)/(-800 - 300) = 2/11-200/-1100 = 2/11You might think that does not correspond to real life, but it is a valid answer. It illustrates the importance of correct presentation. Math is valid only when it describes reality. Mistrakes kill people.

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