answer:Rita made a down payment equal to half the cost of the machine, so she paid 120/2 = <<120/2=60>>60 as a down payment. The remaining balance she needs to pay is 120 - 60 = <<120-60=60>>60. She needs to pay the balance within 10 days, so she needs to pay 60/10 = 6 per day. Therefore, the minimum amount Rita must pay daily in order to own the elliptical machine is 6. 6 The answer is: 6

answer:We want to find the value of X in the given situation. We are given that Kim earned scores of 87, X, and 88 on her first three mathematics examinations. To find the average of her scores, we need to calculate the sum of her scores and divide by the number of scores. The sum of her scores is 87 + X + 88. The number of scores is 3. So, the average of her scores is frac{87 + X + 88}{3}. We are told that Kim receives a score of 90 on the fourth exam. To find out by how much her average will increase, we need to calculate the difference between the new average and the previous average. The new average can be calculated by adding the score of 90 to the sum of her previous scores and dividing by 4 (the total number of exams). The new average is frac{87 + X + 88 + 90}{4}. To find the increase in average, we can subtract the previous average from the new average: frac{87 + X + 88 + 90}{4} - frac{87 + X + 88}{3} To simplify this expression, we can find a common denominator of 12: frac{(87 + X + 88 + 90) cdot 3}{4 cdot 3} - frac{(87 + X + 88) cdot 4}{3 cdot 4} Simplifying further, we have: frac{3(87 + X + 88 + 90)}{12} - frac{4(87 + X + 88)}{12} frac{3(265 + X)}{12} - frac{4(175 + X)}{12} frac{795 + 3X}{12} - frac{700 + 4X}{12} frac{795 + 3X - (700 + 4X)}{12} frac{795 + 3X - 700 - 4X}{12} frac{-X + 95}{12} We are given that the increase in average is 1, so we can set up the equation: frac{-X + 95}{12} = 1 Multiplying both sides of the equation by 12 to eliminate the fraction, we get: -X + 95 = 12 Subtracting 95 from both sides of the equation, we find: -X = -83 Dividing both sides of the equation by -1, we get: X = 83 The value of X is 83. The answer is: 83

answer:We can use the Euclidean algorithm to find the greatest common divisor (GCD) of 1729 and 1768. begin{align*} 1768 &= 1 cdot 1729 + 39 1729 &= 44 cdot 39 + 13 39 &= 3 cdot 13 + 0 end{align*} Since the remainder is 0, the GCD of 1729 and 1768 is the last non-zero remainder, which is boxed{13}. The answer is: 13

answer:If you buy a dozen of doughnuts, it costs 8, so the cost per dozen is 8/1 = 8. If you buy 2 dozens, it costs 14, so the cost per dozen is 14/2 = 7. To find out how much you will save from buying 3 sets of 2 dozens, we need to calculate the total cost of buying 3 sets of 2 dozens and subtract it from the total cost of buying 6 sets of x dozen. The total cost of buying 3 sets of 2 dozens is 3 * 2 * 7 = 42. The total cost of buying 6 sets of x dozen is 6 * x * 8 = 48x. To find the amount you will save, we subtract the total cost of buying 3 sets of 2 dozens from the total cost of buying 6 sets of x dozen: 48x - 42. We are given that the amount you will save is 6, so we can write: 48x - 42 = 6. Solving for x, we get: x = 1. The value of x is 1. 1 The answer is: 1