At the start of the day I had three times as many apples as pears. By the end of the day, after eatingfive apples but no pears, I had twice as many pears as apples.How many pieces of fruit did I have at the start of the day?

Answer 1

Let's use variables to solve the problem. Let's say that at the start of the day, I had "a" apples and "p" pears.

According to the problem, at the start of the day, I had three times as many apples as pears, so:

a = 3p

After eating five apples but no pears, I had:

a - 5 apples
p pears

And according to the problem, I had twice as many pears as apples at the end of the day, so:

p = 2(a-5)

Now we have two equations with two variables. We can substitute the first equation into the second equation:

p = 2(a - 5)
p = 2(3p - 5)
p = 6p - 10
10 = 5p
p = 2

Now that we know that I had 2 pears at the end of the day, we can use the first equation to find out how many apples I had at the start of the day:

a = 3p
a = 3(2)
a = 6

So I had 6 apples and 2 pears at the start of the day.