alex, bob, and mary worked together on project and recieved $11,000. They agreed that bob should recieve $1,000 more than alex and that mary should recieve twic

Question

alex, bob, and mary worked together on a project and received $11,000. They agreed that bob should receive $1,000 more than alex and that mary should receive twice what alex receives. how much should each receive?

Answer 1

Hello Amber,

Let A = Alex, B = Bob, and M = Mary.

 

Then from the first sentence, we have:

A + B + M = 11,000. {Eq 1}

 

From the second sentence:

B = A + 1,000 {Eq 2}

 

 

And from the third sentence, we get:

M = 2A {Eq 3}

 

By substituting Equations 2 and 3 into Equation 1, we end up with:

A + (A + 1,000) + 2A = 11,000

⇒ 4A +1,000 = 11,000 (by combining like terms)

⇒ 4A = 10,000 (by subtracting 1000 from both sides)

⇒ A = 2,500 (by dividing both sides by 4)

 

Therefore,

Alex should receive $2500,

Bob should receive $3500, and

Mary should receive $5000.

 

I hope the above helps.  Should you have any questions or comments regarding it, please feel free to message me.

 

Thank you for posting the question, and have a great evening.

Kind regards,

Michael E.