Question

8. Kyle and his twin sister Katie are playing a number game in which Kyle has to guess the two numbers that

Katie is thinking of. Katie gave Kyle the following two clues about her numbers.


Clue 1: "The sum of the two numbers is 17."

Clue 2: "Five more than twice the smaller number is equal to the larger number."



Part A. Write a system of equations based on Katies' two clues where x is the smaller number and y is the
larger number.


Part B. State what method you would use to solve the system from Part A THEN use that method to identify the two numbers Katie is thinking of. MAKE SURE TO LABEL YOUR ANSWERS

Answer 1

Part A: We can use the given clues to write a system of equations as follows:

x + y = 17 (Clue 1)

y = 2x + 5 (Clue 2)

Part B: To solve the system of equations, we can use the substitution method, which involves solving one equation for one of the variables and substituting the resulting expression into the other equation. In this case, we can solve the second equation for y:

y = 2x + 5

Then we can substitute this expression for y into the first equation:

x + (2x + 5) = 17

Simplifying and solving for x, we get:

3x + 5 = 17

3x = 12

x = 4

Now that we know x is 4, we can substitute this value back into either equation to solve for y. Using the second equation, we get:

y = 2x + 5

y = 2(4) + 5

y = 13

Therefore, the two numbers that Katie is thinking of are x=4 and y=13.

Answer: The smaller number is 4 and the larger number is 13.