Which if any students wrote an expression equivalent to Mrs. Petersons expression

Question

Mrs. Peterson wrote the expression below on the chalkboard for her class. She asked the students to write an equivalent expression using no more than one set of parentheses.

 

8(4x + 3y + 5z) + 4(x - z)

 

Jason wrote 6(6x + 4y + 6z)

Clarissa wrote 32x + 24y -4z

Tom wrote 4(9x + 6y -z)

 

 

Which if any, of the three students wrote an expression that is equivalent to Mrs. Peterson's expression?

 

Show your work to prove which expressions, if any are equivalen.

Answer 1

Using PEMDAS (Order of Operations), you can start to solve ...

 

8 (4x + 3y + 5z) + 4 (x - z)

 32x + 24y + 40z + 4x - 4z

 

36x + 24y + 36z

 

This is the problem just worked out, but now you have to set up the answer like Mrs. Peterson did ...

 

So, when you calculate out what the 3 students wrote, you come up with:

 

Jason wrote 6(6x + 4y + 6z) = 36x + 24y + 36z -- **WINNER!!!!**
Clarissa wrote 32x + 24y -4z -- x and z values just don't match up.
Tom wrote 4(9x + 6y -z) = 36x + 24y - 4z -- z value just doesn't match up.

 

So, Jason wrote the correct expression.

 

 

 

 

 

Answer 2

Let us look at all of them and simplify them:

 

Teacher: 8(4x+3y+5z)+4(x-z) = 36x+24y+36z

 

Jason: 36x+24y+36z

Clarissa: 32x+24y-4z

Tom: 36x+24y-4z

 

Only Jason has an equivalent expression.