Mr. Rozario bought some numbers of apples and oranges in a ratio of 2:3. He gave away 2/3 of the apes to his sister and 23 oranges to his brother. The ratio of the number of apples to the number of oranges that he has now is 3:2. How many apple did he buy?
THESE COMMENTS ARE SO OLD OML
If there are x apples and y oranges, we know that
x/y = 2/3
(1/3 x)/(y-23) = 3/2
Now just solve for x
3/2
To find the number of apples Mr. Rozario bought, we can follow these steps:
Step 1: Determine the ratio between the number of apples and oranges that Mr. Rozario originally bought. The ratio is given as 2:3.
Step 2: Let's assume the number of apples in the original batch is 2x (since the ratio is 2:3).
Step 3: Since Mr. Rozario gave away 2/3 of the apples to his sister, he only has 1/3 left. So, he has (1/3) * (2x) = 2x/3 apples remaining.
Step 4: Mr. Rozario gave away 23 oranges to his brother, which means he has 3x - 23 oranges left.
Step 5: The given ratio of the number of apples to oranges that he has now is 3:2. So, we can set up the following equation using the information from step 3 and step 4:
(2x/3) / (3x - 23) = 3/2
Step 6: Solve the equation to find the value of x:
Cross-multiplying, we get (2x/3) * 2 = (3x - 23) * 3
4x/3 = 9x - 69
Bringing the terms with x to one side, we have:
4x/3 - 9x = -69
(4x - 27x)/3 = -69
-23x/3 = -69
Multiplying both sides by 3 to remove the fraction, we get:
-23x = -207
Dividing both sides by -23, we find:
x = 9
Step 7: Now that we know the value of x is 9, we can determine the number of apples Mr. Rozario bought. We assumed it to be 2x, so the number of apples is 2 * 9 = 18.
Therefore, Mr. Rozario bought 18 apples.