Modeling Equations to Solve a Riddle

2.14.1 Modeling Equations to Solve a Riddle

2.14.1 • Modeling Equations to Solve a Riddle

For questions 1 – 4, use the following scenario to use equations to solve a riddle:

Here is a riddle: “I am thinking of two numbers that add up to 5.678. The difference between them is 9.876. What are the two numbers?”

Name any pair of numbers whose sum is 5.678.

Compare your answer: Your answer may vary, but here is a sample.

2 and 3.678

Name any pair of numbers whose difference is 9.876.

Compare your answer: Your answer may vary, but here is a sample.

10 and 0.124

The riddle can be represented with two equations. Write the equations.

Compare your answer: Your answer may vary, but here is a sample.

Let $x$ and $y$ represent the numbers: $x + y = 5.678$ and $x - y = 9.876$ .

Solve the riddle. Be prepared to show your reasoning.

Compare your answer: Your answer may vary, but here is a sample.

The two numbers are $7.777$ and $- 2.099$ .

Adding the two equations eliminates the $y$ -variable and gives $2 x = 15.554$ or $x = 7.777$ .
Substituting this $x$ -value into either equation gives $y = - 2.099$ .
Graphing the two equations gives two lines that intersect at $(7.777, - 2.099)$ .