Question

If Gary gives $200 to Ricky the ratio of their money will be 1 : 2. If Gary gives $1000 to Ricky their ratio will be 1 : 14. How much does Gary have?

Answer 1

If Gary gives $200 to Ricky the ratio of their money will be 1 : 2. If Gary gives $1000 to Ricky their ratio will be 1 : 14. How much does Gary have?

Suppose, Gary has $X and Ricky has$Y.

If Gary gives $200 to Ricky, Gary has X-200, Ricky has Y+200, ratio of their money will be 1 : 2:

$$\frac {X - 200}{Y + 200} = \frac {1}{2}$$

If Gary gives $1000 to Ricky, Gary has X-1000, Ricky has Y+1000, ratio of their money will be 1 : 14:

$$\frac {X - 1000}{Y + 1000} = \frac {1}{14}$$

From first equation:

$$2 (X - 200) = Y + 200$$

Or:

$$Y = 2 X - 600$$

From second equation:

$$14 (X - 1000) = Y + 1000$$

Substitute $Y = 2X - 600$:

$$14 (X - 1000) = 2X - 600 + 1000$$

Therefore:

$$12 X = 1000 - 600 + 14 * 1000 = 14400$$ $$X = \frac{14400}{12} = \$1200$$

Answer: Gary has $1200.