Consider the equation and its solution.

Question

Negative 15 (x minus box) = 25. Negative 15 x + 30 = 25. Negative 15 x = negative 5. x = one-third.

What number should be in the empty box?
Negative 30
Negative 2
2
30

Answer 1

2

Answer 2

George is building a fence around a rectangular dog run. He is using his house as one side of the run. The area of the dog run will be 240 square feet. The length of the run is 30 feet, and the width is (30 minus x) feet. The diagram below shows his plan.

Recall the formulas for area and perimeter: A = lw and P = 2l + 2w.

A rectangle labeled Dog run has a length of 30 feet and width of (30 minus x) feet.

How many feet of fencing will George need for the dog run?
22 feet
68 feet
76 feet
82 feet

Answer 3

76 feet

Answer 4

Marcel and Floyd are playing games at an arcade. Marcel has $8.25 and is only playing $0.25 games. Floyd has $9.75 and is only playing $0.75 games. Jorge wants to find the number of games after which Marcel and Floyd will have the same amount of money remaining. Jorge’s work is shown below.

Let x = the number of games played.

Equation: 8.25 minus 0.25 x = 9.75 minus 0.75 x. Step 1: negative 1.50 minus 0.25 x = negative 0.75 x. Step 2: negative 1.50 = 0.50 x. Step 3: negative 3 = x.


Jorge knows his answer is incorrect because it does not make sense to have a negative number of games. What is Jorge’s error?
The variable x should represent the amount of money left.
From Step 1 to Step 2, Jorge did not add 0.25x correctly to both sides.
The equation should have sums on both sides.
From Step 2 to Step 3, Jorge should have subtracted 0.50x from both sides.