There is a box that has apples, pears, and oranges. There are 184 apples and pears, an 248 apples and oranges. There are 3 times more oranges than pears. How many apples are in the box?

Expert Answers

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First, we assign variables:

Let x be the number of apples, y be the number of pears, and z be the number of oranges.

We know that there are 184 apples and pears:

`x + y = 184` [1]

We know that there are 248 apples and oranges:

`x + z = 248` [2]

Finally, we know that there are 3 times more oranges than pears:

`z = 3y` [3]

Now, we have three unknowns and three equations, which we can solve using systems.

Using equations 1 and 2, we can eliminate the variable x, by subtracting the two equations:

`x + y - (x + z) = 184 - 248`

`x + y - x - z = -64`

`y - z = -64` [4]

Using equation 3 and 4, we can solve for y and z:

`y - 3y = -64`

`-2y = -64`

`y = 32`

Using, equation 4:

`y - z = -64`

`32 - z = -64`

`-z = -64 - 32`

`-z = -96`

`z = 96`

To solve for x, we can use equation 2:

`x + z = 248`

`x + 96 = 248`

`x = 248 - 96`

`x = 152`

Hence, `x = 152, y = 32, z = 96.`

In short, we have 152 apples.

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