Appearance
question:Armand is playing a guessing game with his dad where he has to guess a number his dad is thinking of. His dad tells him that the number, when multiplied by 3, is three less than twice 51. What is the number?
answer:Let's call the number Armand's dad is thinking of "x" According to the information given, we can set up the equation: 3x = 2(51) - 3 Simplifying the right side of the equation: 3x = 102 - 3 3x = 99 Dividing both sides of the equation by 3: x = 99/3 x = 33 So the number Armand's dad is thinking of is 33. 33 The answer is: 33
question:John is X years younger than his dad. The sum of their ages is 68 years. How many years old is John? If we know the answer to the above question is 22, what is the value of unknown variable X?
answer:We want to find the value of X in the given situation. We are told that John is X years younger than his dad, and the sum of their ages is 68 years. Let's call John's age J and his dad's age D. According to the given information, we can set up two equations: J = D - X (Equation 1) J + D = 68 (Equation 2) To find the value of X, we can solve this system of equations. We can substitute the value of J from Equation 1 into Equation 2: D - X + D = 68 2D - X = 68 Now, we can solve for D by adding X to both sides of the equation and then dividing both sides by 2: 2D = X + 68 D = frac{X + 68}{2} Given that the value of John's age J is 22, we can substitute it into Equation 1 and solve for X: 22 = D - X Substituting the value of D from the previous equation, we get: 22 = frac{X + 68}{2} - X Multiplying both sides of the equation by 2 to eliminate the fraction, we get: 44 = X + 68 - 2X Simplifying, we have: 44 = 68 - X Subtracting 68 from both sides of the equation, we find: -24 = -X Dividing both sides of the equation by -1, we get: X = 24 The value of X is 24. The answer is: 24
question:Village Foods sells good food at a fair price. Their specialty is fresh vegetables. If they get x customers per month, and each customer purchases 2 heads of lettuce for 1 each and 4 tomatoes for 0.5 apiece, then how much money, in dollars, will the store receive in sales of lettuce and tomatoes per month? If we know the answer to the above question is 2000, what is the value of unknown variable x?
answer:Each customer purchases 2 heads of lettuce for 1 each, so the total cost of lettuce per customer is 2 * 1 = 2. Each customer also purchases 4 tomatoes for 0.5 apiece, so the total cost of tomatoes per customer is 4 * 0.5 = 2. The total cost of lettuce and tomatoes per customer is 2 + 2 = 4. If there are x customers per month, then the total sales of lettuce and tomatoes per month is 4 * x. We are given that the total sales per month is 2000, so we can write: 4x = 2000. Dividing both sides by 4, we get: x = 500. The value of x is 500. 500 The answer is: 500
question:Points A, B, Q, D, and C lie on the circle shown and the measures of arcs BQ and QD are 42^circ and 38^circ, respectively. Find the sum of the measures of angles P and Q, in degrees. [asy] import graph; unitsize(2 cm); pair A, B, C, D, P, Q; A = dir(160); B = dir(45); C = dir(190); D = dir(-30); P = extension(A,B,C,D); Q = dir(0); draw(Circle((0,0),1)); draw(B--P--D); draw(A--Q--C); label("A", A, NW); label("B", B, NE); label("C", C, SW); label("D", D, SE); label("P", P, W); label("Q", Q, E); [/asy]
answer:We know that the measure of an angle formed by two intersecting chords is equal to half the sum of the measures of the intercepted arcs. Since arcs BQ and QD have measures 42^circ and 38^circ, respectively, we can conclude that angles BPQ and QPD each have measures frac{1}{2}(42^circ+38^circ)=boxed{40^circ}. The answer is: 40