Together Kate and Matt have 47 cards. If Kate and Zach combine cards they have 126. If Matt and Zach combine they have 93. How many cards does Matt have

Matt has 7 cards.

Step-by-step explanation:

Let K, M and Z represent number of cards that Kate, Matt and Zach have.

We have been given that together Kate and Matt have 47 cards. We can represent his information in an equation as:

We are also told that Kate and Zach combine cards they have 126. We can represent his information in an equation as:

Further, Matt and Zach combine they have 93. We can represent his information in an equation as:

Upon subtracting equation (3) from equation (2), we will get:

Upon substituting this value in equation (1), we will get:

Therefore, Matt has 7 cards.

Matt has 7 cards.

Step-by-step explanation:

Let x represent the number of cards that Kate has.

Let y represent the number of cards that Matt has.

Let z represent the number of cards that Zach has.

Together Kate and Matt have 47 cards. This means that

x + y = 47

y = 47 - x

If Kate and Zach combine cards they have 126. This means that

x + z = 126

z = 126 - x

If Matt and Zach combine they have 93. This means that

y + z = 93 - - - - - - - - - 1

Substituting y = 47 - x and z = 126 - x into equation 1, it becomes

47 - x + 126 - x = 93

47 + 126 - x - x = 93

173 - 2x = 93

2x = 173 - 93

2x = 80

x = 80/2 = 40

The number of cards that Matt has is

y = 47 - x = 47 - 40

y = 7