# Question 1: The sum of two consecutive even integers is 70. Find the numbers. Question 1 options: 28 and 32 30 and 40 33 and 37 34 and 36 Question 2: Cat is 5 less than twice Dog's age. Cat is 11 years old. Find Dog's age. Question 2 options: 8 7 6 5 Question 3: The sum of three consecutive numbers is 46. Find the numbers. Question 3 options: 19, 20, and 21 20, 21, and 22 21, 22, and 23 22, 23, and 24 Question 4: What is the equation for the sum of three consecutive even numbers totaling 198. Question 4 options: n+n+1+n+2=198 n+n+2+n+4=198 3n=198 n+3=198 Question 5: What is the equation for the sum of four consecutive numbers totaling 86. Question 5 options: 4n=86 n+4=86 n+n+1+n+2+n+3=86 n+n+2+n++4+n+6=86 Question 6: The perimeter of a rectangle is 150 cm. The length is 15 cm greater than the width. Find the dimensions Question 6 options: length = 45 and width = 30 length = 30 and width =45 length = 75 and width = 60 length =60 and width =75 Question 7: A couch cost 5. If the state has a 10% sale's tax. What was the price of the couch before taxes? Question 7 options: 785 0 735 700 Question 8: A bicycle and a bicycle helmet cost 240 dollars. How much did each cost, if the bicycle cost 5 times as much as the helmet? Question 8 options: bike = 0 and helmet = bike = 0 and helmet = bike = 0 and helmet = bike = 0 and helmet = Please help.

Question (1): Assume that the first number is n. Since the two number are consecutive even numbers, this means that the second number is n + 2 We know that the sum of the two numbers is 70. This means that: n + n + 2 = 70 2n + 2 = 70 2n = 68 n = 68/2 n = 34 This means that the two numbers are: 34 and 34+2 = 36 .......> last option Question (2): Assume dog's age is x. We know that cat's age is 5 less than twice dog's age. This means that: cat's age = 2x - 5 We know that cat's age is 11, therefore: 11 = 2x - 5 11 + 5 = 2x 16 = 2x x = 16/2 = 8 Dog's age is 8 .......> first option Question (3): The three numbers are consecutive. This means that we can assume the numbers to be n, n+1 and n+2. We know that their sum is 46. Therefore: n + n + 1 + n + 2 = 46 3n + 3 = 46 3n = 43 n = 43/3 The three numbers are 43/3 , 46/3 and 49/3 .......> none of the given options in correct Question (4): The three consecutive numbers are all even. This means that we can assume the numbers to be n , n+2 and n+4 We know that their sum is 198. This means that: n+n+2+n+4 = 198 .........> second option Question (5): The four consecutive numbers can be assumed as n, n+1 , n+2 and n+3. We know that their sum is 86. Therefore: n + n+1 + n+2 + n+3 = 86 .......> third option Question (6): Assume the width is w. We know that the length is 15 cm greater than the width. This means that: length = w + 15 Now, we have: perimeter = 2(length + width) 150 = 2 (15 + w + w) 75 = 15 + 2w 60 = 2w w = 60/2 w = 30 cm This means that: length = 15 _ 30 = 45 cm Based on the above, the dimensions of the rectangle are: length = 45 cm and width = 30 cm .......> first option Question (7): Assume original price before taxes is x Total price = original price + taxes 825 = x + 0.1x = 1.1 x x = 825/1.1 x = $750 .........> second option Question (8): Assume cost of helmet is x and that cost of bicycle is 5x. We know that the total is 240. This means that: 240 = x + 5x = 6x x = 240/6 x = 40 This means that: price of helmet =$40 price of bicycle = 5(40) = \$200 ..........> first option Hope this helps :)