Make your own equation.

1. A number is 6 times another number. The sum of the two numbers is 56.

@. Donna has twice as many coins as Cathy. When Donna gives Cathy 2 coins, they each have the same number. How many coins do they each have?
Let the number of coins that Cathy has be x.

first number : x

second number : 6x

equation: x + 6x = 56

now try the same thing for your second problem

Donna = x coin

Cathy = y coins

x=2y
x-2=y+2
2y-2=y+2

4,16

Sure!

For the first equation:
Let's represent the first number as 'x' and the second number as 'y'.

According to the given information, "A number is 6 times another number." This can be expressed as:
x = 6y

The second piece of information states that "The sum of the two numbers is 56." This can be expressed as:
x + y = 56

Therefore, the equation system to solve for 'x' and 'y' is:
x = 6y
x + y = 56

Now, let's move on to the second equation:

Let's represent the number of coins that Cathy has as 'x', and the number of coins that Donna has as 'y'.

According to the given information, "Donna has twice as many coins as Cathy." This can be expressed as:
y = 2x

It is also stated that "When Donna gives Cathy 2 coins, they each have the same number." We can express it as:
(x + 2) = (y - 2)

Therefore, the equation system to solve for 'x' and 'y' is:
y = 2x
(x + 2) = (y - 2)

By solving this system of equations, we can find the values of 'x' and 'y', which will represent the number of coins Cathy and Donna have, respectively.