Question

There are 32 more apple than oranges in a box. 3/5 of the oranges and 1/3 of the apples are overripe. If the number of overripe apples and the number of oranges is the same, how many pieces of overripe fruit are there?

Answer 1

Hello!

The answer is:

There is a total of 48 overripe fruit.

Why?

To calculate the number of pieces of overripe fruit we have, we need to write two equations to create a relationship between the number of apples and oranges.

Let be "x" the number of oranges, so:

`Oranges=x\\Apples=x+32`

Now, we know that 3/5 of the oranges and 1/3 of the apples are overripe, so:

`OverripeApples=(1)/(3)(x+32)\\\\OverripeOranges=(3)/(5)(x)`

Then, we have a condition that states that the number of overripe apples and overripe oranges is the same, so:

`(1)/(3)(x+32)=(3)/(5)(x)`

`(1)/(3)(x)+(1)/(3)(32)=(3)/(5)(x)`

`(1)/(3)(32)=(3)/(5)(x)-(1)/(3)(x)`

`(1)/(3)(32)=(3x*3-1*x)/(15)=(9x-5*x)/(15)=(4x)/(15)`

`(32)/(3)=(4x)/(15)`

`(32*15)/(3)=4x`

`(480)/(3)=4x`

`160=4x`

`(160)/(4)=x`

`40=x`

Therefore, we have that there are 40 oranges and 72 apples (40+32).

Now, calculating the number of overripe oranges and apples, we have:

`OverripeApples=(1)/(3)(72)=24\\\\OverripeOranges=(3)/(5)(40)=24`

Hence, we have that there are 24 pieces of overripe oranges and 24 pieces of overripe apples. It means that there is a total of 48 overripe fruit.

Have a nice day!