Question

The ratio of George's money and Tia's

Answer 1

Answer: 28 dollars

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Explanation:

G = amount of money George starts with

T = amount of money Tia starts with

Initially the ratio of their money is 9:4 so G/T = 9/4. Solve for G to get G = (9/4)T.

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After George spends 24 dollars he's left with (G-24) dollars. Tia gains 11 dollars so she has (T+11) dollars. They have the same amount of money after these two events occur, so G-24 = T+11.

Plug in G = (9/4)T and solve for T

G-24 = T+11

(9/4)T-24 = T+11 ... replace G with (9/4)T

4*[  (9/4)T-24 ] = 4*[ T+11 ] ... multiply both sides by 4 to clear out fraction

9T - 96 = 4T + 44 ... distribute

9T - 4T = 44 + 96

5T = 140

T = 140/5

T = 28

Tia started off with 28 dollars. We could stop here because your teacher is only asking about Tia's initial amount.

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If you want to find how much George started with, then plug T = 28 into G = (9/4)T to get...

G = (9/4)T

G = (9/4)*28

G = 2.25*28

G = 63

George started off with 63 dollars

The ratio of 63:28 reduces to 9:4 after dividing both parts by the GCF 7. This confirms the first fact we're given.

Notice how 63 drops to 63-24 = 39 after George spends $24. At the same time, Tia's amount increases to 28+11 = 39, which is the same as George's updated amount. Both facts match the description, so we have confirmed the answer.