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question:Mrs. Dunbar was creating floral arrangements for her niece's wedding. She needed to make 5 bouquets and 7 table decorations. She uses 12 white roses in each table decoration and x white roses in each bouquet. She needs 109 white roses in total to complete all bouquets and table decorations. What is the value of unknown variable x?
answer:To solve this problem, we need to determine the value of x, which represents the number of white roses used in each bouquet. Let's break down the information given: Number of bouquets: 5 Number of table decorations: 7 Number of white roses used in each table decoration: 12 Number of white roses used in each bouquet: x Total number of white roses needed: 109 We can set up the equation as follows: Number of white roses used in each bouquet * Number of bouquets + Number of white roses used in each table decoration * Number of table decorations = Total number of white roses needed x * 5 + 12 * 7 = 109 Let's simplify and solve for x: 5x + 84 = 109 To isolate x, we subtract 84 from both sides of the equation: 5x + 84 - 84 = 109 - 84 5x = 25 To solve for x, we divide both sides of the equation by 5: x = 25 / 5 x = 5 The value of x is 5. 5 The answer is: 5
question:w many four-digit positive integers are palindromes?
answer:A palindrome is a number that reads the same backward as forward. For a four-digit palindrome, the first and last digits must be the same, and the second and third digits must be the same. There are 9 choices for the first digit (1 through 9), and 10 choices for the second digit (0 through 9). Once the first two digits are chosen, the last two digits are determined. Therefore, there are 9 cdot 10 = boxed{90} four-digit palindromes. The answer is: 90
question:The notation [x] stands for the greatest integer that is less than or equal to x. Calculate [-1.2].
answer:Since -2 is the greatest integer that is less than or equal to -1.2, we have [-1.2] = boxed{-2}. The answer is: -2
question:f a,b,c satisfy the system of equations begin{align*}b + c &= 12-3a a+c &= -14 - 3b a+b &= 7 - 3c, end{align*} what is 2a + 2b + 2c?
answer:Adding all three equations, we have 2a + 2b + 2c = (b + c) + (a + c) + (a + b) = 12 - 3a + (-14 - 3b) + (7 - 3c) Simplifying, we get 2a + 2b + 2c = -3a - 3b - 3c + 5 Rearranging terms, we have 5a + 5b + 5c = 5 Dividing both sides by 5, we get a + b + c = 1 Therefore, 2a + 2b + 2c = 2(1) = boxed{2}The answer is: 2