What's the Value of a Fox? 3.4 Reasoning w/Linear Equations

Write an equation to represent this situation. Use f to represent the value of a fox.

• f = fox

• 3f + 32 = f + 22

• 3f + 22 = f + 32

• 3x + 32 = x + 22

Answer explanation

The equation 3f + 32 = f + 22 correctly represents the situation by balancing the value of three foxes plus 32 with the value of one fox plus 22, making it the right choice.

Do foxes have a positive or negative impact on your score? How do you know?

• Positive impact

• Negative impact

• No impact

• Not sure

How many points is a fox worth?

• -5 points

• 5 points

• -10 points

• 10 points

Who is winning at this point? By how much?

• Britney by 10 points

• Hugh by 5 points

• Britney by 3 points

• Hugh by 8 points

What is the value of a mushroom?

• -2 points

• -10 points

• 2 points

• 10 points

Two climbers are on a rock-climbing wall. Climber A is at a height of 48 feet and descending at a rate of 3 feet per second. Climber B is on the ground and is ascending at a rate of 2.5 feet per second. a. Write an equation that could be used to solve for the time in seconds, s, when the climbers are at the same height.

• 48 - 3s = 2.5s

• 48 + 3s = 2.5s

• 48 - 2.5s = 3s

• 48 + 2.5s = 3s

Answer explanation

Climber A's height decreases by 3s, so their height is 48 - 3s. Climber B's height increases by 2.5s, so their height is 2.5s. Setting these equal gives the equation 48 - 3s = 2.5s, which is correct.

What is the distance between the two climbers initially?

• 3 feet

• 2.5 feet

• 48 feet

• 0 feet

How fast is the distance between them decreasing, in feet per second?

• 5 feet per second

• 10 feet per second

• 15 feet per second

• 20 feet per second

After how many seconds will the climbers be at the same height?

• 5.5 seconds

• 8.73 seconds

• 10 seconds

• 48 seconds

Answer explanation

The climbers will be at the same height after 30 seconds because their rates of ascent and starting heights allow them to meet at that time, making 30 seconds the correct answer.

What is the difference between the amounts (pounds) of pet food for Corie?