Question

Donnie deli man delivered 595 box lunches for the robotics convention. There were 20 more turkey sandwiches then roast beef. There were twice as many roast beef has PB&J. How many of each type of BoxLunch did Donnie delivered?

Answer 1

250 turkey sandwiches were delivered.

There were 230 roast beef delivered.

115 PB&J were delivered.

Explanation:

This question is solved using a system of equations.

I am going to say that:

x is the number of turkey sandwiches.

y is the number of roast beef.

z is the number of PB&J.

Donnie delivered 595 box lunches

This means that
`x + y + z = 595`

There were 20 more turkey sandwiches then roast beef.

This means that
`x = y + 20`

There were twice as many roast beef has PB&J.

This means that
`y = 2z`.

So in the second equation, we have that
`x = 2z + 20`

Replacing this in the first equation:

`x + y + z = 595`

`2z + 20 + 2z + z = 595`

`5z = 575`

`z = (575)/(5)`

`z = 115`

115 PB&J were delivered.

`x = 2z + 20 = 2*115 + 20 = 250`

250 turkey sandwiches were delivered.

`x = y + 20`

So

`y = x - 20 = 250 - 20 = 230`

There were 230 roast beef delivered.