Question 1

Which of the following is the correct first step when solving an applied problem, according to the recommended process?

Accepted Answer

Read the problem carefully to understand what is given and what is to be found.

Question 2

A puzzle piece in the shape of a triangle has a perimeter of $$30 cm. $$Two sides are each twice as long as the shortest side. If $$x$$ represents the length of the shortest side, which equation correctly models the perimeter?

Accepted Answer

$$x + 2x + 2x = 30$$

Question 3

What is the length of the shortest side of the triangle puzzle piece described above?

Accepted Answer

$$6 cm$$

Question 4

After solving an equation in an applied problem, what is the next recommended step?

Accepted Answer

State the answer to the problem and consider if it seems reasonable.

Question 5

If the sides of a triangle are $$x$$, $$2x$$, and $$2x$$ and the perimeter is $$30 cm$$, what is the value of $$x$$?

Accepted Answer

$$x = 6$$

Question 6

Which step in solving an applied problem involves expressing other unknown values in terms of the variable?

Accepted Answer

Step 2: Assign a variable

Question 7

A triangle has sides of lengths $$x$$, $$2x$$, and $$2x. If $$the perimeter is increased to $$36 cm$$, what is the new length of the shortest side?

Accepted Answer

$$x = 9$$

Question 8

Which of the following best describes the purpose of checking the answer in the words of the original problem?

Accepted Answer

To verify that the solution makes sense in the context of the problem.

Question 9

If you mistakenly set up the equation for the triangle puzzle piece as $$x + x + 2x = 30$$, what would be the value of $$x$$?

Accepted Answer

$$x = 7.5$$

Question 10

Which of the following is NOT a recommended step in solving an applied problem?

Accepted Answer

Guess the answer based on intuition.

Question 11

A triangle has sides $$x$$, $$2x$$, and $$2x. If $$the shortest side is $$8 cm$$, what is the perimeter?

Accepted Answer

$$32 cm$$

Question 12

Which step involves writing down what the variable represents in the context of the problem?

Accepted Answer

Step 2: Assign a variable

College Algebra Study Guidance: Solving Applied Problems and Triangle Perimeter Modeling

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