Mr. Rozario bought some oranges and some apples. The ratio of oranges to apples is 2:5. He gave 3/4 to his sister and 34 oranges to his brother. He now has a ratio of 2:3. How many oranges and apples did he buy?

He bought 544 oranges and 1,360 apples

Step-by-step explanation:

Here, we want to know the number of oranges and apples bought

Let the number of oranges be x and the number of apples be y

Looking at their ratios;

x:y = 2:5

so;

x/y = 2/5

2y = 5x ••••••(i)

Now, he lost 3/4 of the apples ( by giving out)

What would be left with him is (1-3/4) = 1/4 * y = 0.25y

What is left with him out if the oranges will be; x-34

So now;

0.25y/x-34 = 2/3

3(0.25y) = 2(x-34) •••••••(ii)

From i, y = 5x/2 = 2.5x

Putting this into ii above, we have

3(0.25)(2.5x) = 2x - 68

1.875x = 2x-68

2x-1.875x = 68

0.125x = 68

x = 68/0.125

x = 544

But y = 2.5x

y = 2.5 * 544 = 1,360