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 $825. if the state has a 10% sale's tax. what was the price of the couch before taxes?
question 7 options:
785
$750
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 = $200 and helmet = $40
bike = $160 and helmet = $80
bike = $120 and helmet = $60
bike = $100 and helmet = $90
.

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 :)

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