# 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?

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### 2 Answers

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.

There is a box that has apples, pears, and oranges. The total number of apples and pears is 184 and the total number of apples and oranges is 248. The box thrice as many oranges as pears.

If x is the number of apples,

x + pears = 184

pears = 184 - x

x + oranges = 248

oranges = 248 - x

Now there are thrice as many oranges as pears:

248 - x = 3*(184 - x)

248 - x = 552 - 3x

2x = 304

x = 152

This gives the number of apples in the box as 152.