Mr. Kwon has just enough money to buy only 20 mangoes or only 30 oranges. If he wants to buy equal numbers of mangoes and oranges together, how many of each type can he buy with the money?

Answer 1

Let x be the amount of money he has.

Let m be price of one mango.

Let o be price of one orange.

Suppose he can just buy n of each fruit.

Then:

n * m + n * o = x

You know 20 mangoes cost x

so

m = x / 20

likewise

o = x / 30

So you have:

n * m + n * o = x

n * x / 20 + n * x / 30 = x Divide both sides by x

n / 20 + n / 30 = 1

3 * n / 3 * 20 + 2 * n / 2 * 30 = 1

3 n / 60 + 2 n / 60 = 1

5 n / 60 = 1

5 n / 5 * 12 = 1

n / 12 = 1 Multiply both sides by 12

n = 12

He can buy 12 mangos and 12 oranges.