Linear Inequalities in One Unknown

Question

Question 1: If two times the sum of two consecutive even numbers is greater than 94, what is the smallest possible value of the larger number?

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Answer=26

Question 2:The sum of weights of Miss Wong and Mr Ho is not greater than 124kg.If the weight of Mr Ho is 1.5times the weight of Miss Wong, find the maximum possible weight of Mr Ho.

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Answer=74.4kg

Question 3: If the sum of two consecutive old numbers is less than 49, what is the largest possible value of the smallest number?

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Answer=13

Question 4: Dick wants to join a golf club.The golden club membership costs $350 per person and $26 will be charged for each hour of playing time.The silver club membership costs $200 per person and $40 will be charged for each hour of playing time. Let x be the number of hours that Dick plans to play.

hints= the amount Dick has to pay if he joins ( in terms of x)

i.the golden club membership $(350+26x)

ii.the Silver club membership $(200+40x)

Q.At least how many hours should Dick play so that it costs less to join the Golden Club membership than the Silver Club membership?

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Answer=11hours

Question 5:Mary plans to spend at most 2hours for running and cycling on a sunny day.She first cycles at a constant speed of 16km/h and then runs at a constant speed of 8km/h. It is known that the distance that Mary cycles is greater than that Mary runs by 2 km. At most how far does Mary cycle?

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Answer=12km

I want to step by step for these 5 methods please. It would be a pleasure if you could help me. Thx

Answer 1

question 1: 94/2 = 47, the even consecutive numbers are 46 and 48

48 is the smallest possible larger number if they sum to 94

but to be greater than 94, the smallest possible larger numbrr is 50

question 3: there are no odd numbers that sum to 49. add any 2 odd numbers and they sum to an even number 49/2 = 24.5. 25 and 27 are the smallest odd numbers that sum to greater than 49

27 is the smallest larger odd number

question 5: Mary cycles at least 25 km

2 hours times (16+8) = 2(24) = 48 km total distance running and cycling

25+23 = 48. 25=23+2, as she cycles 2 km more than she runs