Solve for x in the following equation: 3(2 - 3x) = x - 4.
Remember to use the correct order of operations. One of the easier ways to remember the order is to use "PEMDAS," or "Please Excuse My Dear Aunt Sally." The operation is represented by each letter in PEMDAS: Parentheses (Simplify what's inside the parentheses first) Exponents Multiplication Division Addition Subtraction Following that mnemonic, the first step to take is to simplify the left side of the equation by expanding it. You multiply the term outside the brackets by each term inside the bracket. (1) 3(2 - 3x) => 3*2 - 3*3x = 6 - 9x (2) 6 - 9x = x - 4 We would then like to combine common terms. (3) 6 + 4 - 9x = x - 4 + 4 (4) 10 - 9x = x (5) 10 - 9x + 9x = x + 9x (6) 10 = 10x Notice that in an equation problem like this, you must do the same thing to both sides of the equation. In this problem, we wanted to combine the constants 6 and -4 by adding 4 to both sides. This removes the constant from the right side of the equation. We do the same with the x variables as well. However, we are looking for x and not 10x. We can find x by dividing both sides by 10: (7) 10/10 = (10x)/10 (8) 1 = x Therefore, x is 1.
The ratio between students who brought food from home and students who bought food at the cafeteria is 3:6. What is the percentage of students who brought food from home? Round to the nearest percentage point.
In order to convert a ratio to a percentage, you must remember to obtain the total by adding both numbers in a ratio. In this case, the total will be 9. (1) 3+6= 9 *NOTE: This does not mean there are 9 students in the classroom. Please do not make this assumption unless the problem tells you so. You will then need to divide the number of students who brought food from home by the total. (2) 3/9 = 0.33333 repeating To get the percentage we want, we need to multiply the decimal by 100. This will give us 33.3333 repeating, which would be the percentage of students who brought food from home. However, the question asks you to round to the nearest whole percentage point. Whenever the value being rounded is 4 or under, you round down to a zero. Therefore, our answer to the question is 33 percent.
Bob has $40 to spend at a supermarket. He spends twice as much on steak than he does on vegetables, and spends a quarter of his total budget on snacks and candy. How much did Bob spend on vegetables?
Because Bob has spent a quarter (40 * 1/4 = 10) of his total budget on snacks and candy, there is only $30 (40-10 = 30) left over for steak and vegetables. Now, we can use an algebraic equation to explain the relationship among the remaining information. If we define the money spent on vegetables as x, steak will be 2x (twice as much). Adding the cost of vegetables (x) and steak (2x) should give us the $30 remaining after snacks and candy. We can write this in equation form and solve it: (1) x + 2x = 30 (2) 3x = 30 (3) x = 10, therefore Bob spent $10 on vegetables