write an equation that represents the given condition in each statement

Question

1. the sums of numbers is 36.
2. the difference of 2 numbers is 21
3. hannah's age is three more than twice angel's age
4. in a class, twice the number of boys exceeded the number of girls by 12.
5. a 96-inch ribbon is cut into two so that one piece is 12 inches shorter than the other piece.

Answer 1

Let's create an equation that represent each of the 5 given conditions below (questions bolded, equations italicized):

The sums of numbers is 36.

Assuming we have 2 numbers, we can write the equation as:

x + y = 36

The difference of 2 numbers is 21.

Assuming again that we have two numbers, we can use a similar approach:

x - y = 21

Hannah's age is three more than twice Angel's age.

If we represent Angel's age with the variable "a", and Hannah's age with the variable "h", then we get the equation:

(2 * a) + 3 = h

In a class, twice the number of boys exceeded the number of girls by 12.

If the number of boys is "B" and the number of girls is "G", then our equation will look like this:

(2 * B) - G = 12

A 96-inch ribbon is cut into two so that one piece is 12 inches shorter than the other piece.

We know that one piece of the ribbon is 12 inches larger than the other. From this, we can assign both pieces a variable. For the shorter piece, we assign it the variable "S". For the larger piece, we assign it an expression using "S" again, this time adding 12 (S + 12). Adding these two elements together results in the equation:

S + (S + 12) = 96