Question

4. Diego is thinking of two positive numbers. He says, “If we triple the firstnumber and double the second number, the sum is 34."4a. Write an equation that represents this clue. Then, find two possiblepairs of numbers Diego could be thinking of. *4b. Diego then says, "If we take half of the first number and double thesecond, the sum is 14. "Write an equation that could represent thisdescription."

Answer 1

Solution:

The question is an example of word problems.

We develop the sentences into mathematical equations to get the possible solutions.

Part A:

From the statements given, the following can be deduced,

$\begin{gathered} \text{Let x and y be the two positive numbers} \\ \text{If we triple the first number, this means;} \\ 3\times x=3x \\ \\ \text{If we double the second number, this means}; \\ 2\times y=2y \\ \\ \text{The sum is 34, this means;} \\ 3x+2y=34 \end{gathered}$

Therefore, the equation that represents the clue is 3x + 2y = 34

To find the two possible pairs of numbers Diego could be thinking of,

We can plot the equation on a graph showing the straight line.

The points on the straight line satisfy the equation.

However, the pairs that are positive numbers (positive integers) are shown;

Hence, the possible pairs of numbers Diego could be thinking of in the form (x,y) are;

$(0,17),(2,14),(4,11),(6,8),(8,5),(10,2)$

Part B:

From the statements given, the following can be deduced,

$\begin{gathered} \text{Let x and y be the two positive numbers} \\ \text{If we take half of the first number, this means;} \\ \frac{1}{2}\times x=\frac{x}{2} \\ \\ \text{If we double the second number, this means}; \\ 2\times y=2y \\ \\ \text{The sum is 14, this means;} \\ \frac{x}{2}+2y=14 \end{gathered}$

Therefore, the equation that could represent the description is;

$\frac{x}{2}+2y=14$