A triangle has a perimeter of 50. If 2 of its sides are equal and the third side is 5 more than the equal sides, what is the length of the third side?
Step 1: Assign variables: Let x = length of the equal side Sketch the figure Step 2: Write out the formula for perimeter of triangle. P = sum of the three sides Step 3: Plug in the values from the question and from the sketch. 50 = x + x + x + 5 Combine like terms 50 = 3x + 5 Isolate variable x 3x = 50 – 5 3x = 45 x =15 Be careful! The question requires the length of the third side. The length of third side = 15 + 5 =20 Answer: The length of third side is 20
Jane spent $42 for shoes. This was $14 less than twice what she spent for a blouse. How much was the blouse?
Every word problem has an unknown number. In this problem, it is the price of the blouse. Always let x represent the unknown number. That is, let x answer the question. Let x, then, be how much she spent for the blouse. The problem states that "This" -- that is, $42 -- was $14 less than two times x. Here is the equation: 2x − 14 = 42. 2x = 42 + 14 2x = 56. x = 56/2 x = 28. The blouse cost $28.
There are b boys in the class. This is three more than four times the number of girls. How many girls are in the class?
Let x represent the unknown number that you are asked to find: Let x be the number of girls.(Although b is not known, it is not what you are asked to find.) The problem states that "This" -- b -- is three more than four times x: 4x + 3 = b. Therefore, 4x = b − 3 x = (b − 3)/4 The solution here is not a number, because it will depend on the value of b. This is a type of "literal" equation, which is very common in algebra.