Consider the equation and its solution.
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
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
76 feet
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.
To solve for the missing number in the box, we can follow the given equation step by step.
Negative 15 (x - box) = 25
To simplify, we distribute the negative 15 to both terms inside the parentheses:
Negative 15 x - 15(box) = 25
Now, we rearrange the equation to isolate the variable:
Negative 15 x - 15(box) - 15(box) = 25 - 15(box)
Negative 15 x - 30(box) = 25
Next, we simplify the equation further:
Negative 15 x - 30(box) = 25
Now, comparing this equation with the given equation in the problem "Negative 15 x + 30 = 25," we can see that the two equations are similar except for the sign of the constant term. In the given equation, the constant term is positive 30, while in the equation above, it is negative 30.
Therefore, the number that should be in the empty box is Negative 2.
To find the number that should be in the empty box, we can work backwards from the solution of the equation.
The given equation is: Negative 15 (x - box) = 25.
By distributing the Negative 15, we get: -15x + 15(box) = 25.
Next, we want to isolate the variable on one side of the equation. Let's rearrange the equation: -15x = 25 - 15(box).
To simplify further, we can subtract 25 and divide by -15: x = (25 - 15(box)) / -15.
Given that the solution is x = one-third, we can substitute that into the equation: one-third = (25 - 15(box)) / -15.
To get rid of the fraction, we can multiply both sides of the equation by -15: -15 * one-third = 25 - 15(box).
The left side simplifies to: -5 = 25 - 15(box).
Now, we need to isolate the box. Let's rearrange the equation: 15(box) = 25 + 5.
Simplifying further, we get: 15(box) = 30.
Finally, to solve for the box, we can divide both sides of the equation by 15: (box) = 30 / 15.
Therefore, the number in the empty box should be 2.