Q: If the sum of the three numbers is 300, and the first number is $$x$$, which of the following systems of equations could be used to solve for all three numbers?

$$\begin{cases} y = 6x \\ z = 100 + x \\ x + y + z = 300 \end{cases}$$

Question 1

Let $$x be $$the first number. If the second number is 6 times the first number and the third number is 100 more than the first number, which equation correctly represents the sum of the three numbers being 300?

Accepted Answer

$$x + 6x + (100 + x) = 300$$

Question 2

After combining like terms in the equation $$x + 6x + 100 + x = 300$$, what is the resulting equation?

Accepted Answer

$$8x + 100 = 300$$

Question 3

What is the value of $$x$$ after solving $$8x + 100 = 300$$?

Accepted Answer

$$x = 25$$

Question 4

If the first number is $$x = 25$$, what is the value of the second number, given it is 6 times the first number?

Accepted Answer

$$150$$

Question 5

Given the first number is $$25$$, what is the value of the third number, which is 100 more than the first number?

Accepted Answer

$$125$$

Question 6

Which of the following correctly checks the sum of the three numbers found in the problem?

Accepted Answer

$$25 + 150 + 125 = 300$$

Question 7

If the sum of three numbers is 300, and the second number is 6 times the first, which of the following is the correct expression for the third number?

Accepted Answer

$$100 + x$$

Question 8

Which step is necessary to isolate $$x in $$the equation $$8x + 100 = 300$$?

Accepted Answer

Subtract 100 from both sides

Question 9

If the first number was instead $$x = 30$$, what would the sum of the three numbers be using the same relationships?

Accepted Answer

$$310$$

Question 10

Which of the following best describes the problem-solving strategy used in the example?

Accepted Answer

Define variables, translate words to algebraic expressions, set up an equation, solve, and check the answer.

Question 11

Suppose the third number was instead 200 more than the first number. What would be the new equation for the sum?

Accepted Answer

$$x + 6x + (200 + x) = 300$$

Question 12

If the sum of the three numbers is 300, and the first number is $$x$$, which of the following systems of equations could be used to solve for all three numbers?

Accepted Answer

$$\begin{cases} y = 6x \ z = 100 + x \ x + y + z = 300 \end{cases}$$

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