The ratio of George's money and Tia's money was 9 : 4. After George spent
$24 and Tia collected $11, the amounts
money they had are the same. How
much
money
did Tia have at first?

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.

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.

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.

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step-by-step explanation: