Michael wants to buy a new 4K HD TV. The cheapest TV is advertised as $1100$1100. He has saved $300$300 already and has a part-time job earning $160$160 per week. How many weeks will it take before he has saved up enough to buy the cheapest TV?
Since Michael needs to save up at least $1100$1100 to buy the TV, he must keep earning $160$160 per week until he has greater than or equal to$1100$1100.
Hence, the inequality can be written as:
300+160n300+160n
≥≥
11001100
Next, make sure that only nn is on the left side
300+160n300+160n
≥≥
11001100
300+160n300+160n-300−300
≥≥
11001100-300−300
Subtract 300300 from both sides
160n160n÷160÷160
≥≥
800800÷160÷160
Divide both sides by 160160
nn
≥≥
55
n≥5n≥5
Question 2 of 5
2. Question
A hard drive holds about 7575 hours of movie videos. So far it has 5252 hours. You estimate that each movie is 22 hours long. How many movies can we transfer on top of the movies that are already in the hard drive?
Hours already on hard drive=52Hours already on hard drive=52
Number of hours per movie=2Number of hours per movie=2
Number of movies=nNumber of movies=n
First, form an inequality from the problem
Since the hard drive only has a capacity of 7575 hours, the total number of 22 hour movies to be added on top of the 5252 hours worth that is already on the hard drive must be less than or equal to7575.
Hence, the inequality can be written as:
52+2n52+2n
≤≤
7575
Next, make sure that only nn is on the left side
52+2n52+2n
≤≤
7575
52+2n52+2n-52−52
≤≤
7575-52−52
Subtract 5252 from both sides
2n2n÷2÷2
≤≤
2323÷2÷2
Divide both sides by 22
nn
≤≤
11.511.5
Since we can only add a whole movie and we cannot go over 7575, we need to round down the answer to n≤11n≤11
n≤11n≤11
Question 3 of 5
3. Question
James currently weighs 108108 kg. He wants to weigh less than 9090 kg. If he can lose an average of 112112 kg per week through exercise and diet, how long will it take to reach his goal?
Jame’s current weight=108kgJame’s current weight=108kg
Jame’s goal=90kgJame’s goal=90kg
Weight lost per week=112kgWeight lost per week=112kg
Number of weeks=nNumber of weeks=n
First, form an inequality from the problem
Since James wants to weigh less than 9090 kg, he must keep losing 112112 every week until he weighs less than9090 kg.
Hence, the inequality can be written as:
108-112n108−112n
<<
9090
Next, make sure that only nn is on the left side
108-112n108−112n
<<
9090
108-112n108−112n-108−108
<<
9090-108−108
Subtract 108108 from both sides
-112n−112n÷(-112)÷(−112)
<<
-18−18÷(-112)÷(−112)
Divide both sides by -112−112
nn
>>
1212
Flip the inequality
nn>>1212
Question 4 of 5
4. Question
A medium-sized bag of potatoes weighs 11 kg more than a small bag. A large bag weighs 44 kg more than a small bag. If the total weight is at most 1414 kg, what is the most that a small bag could weigh?
Total weight of bags=Total weight of bags= maximum of 1414
Small-sized bag(S)=sSmall-sized bag(S)=s
Medium-sized bag(M)=s+1Medium-sized bag(M)=s+1
Large-sized bag(L)=s+4Large-sized bag(L)=s+4
First, form an inequality from the problem
The total weight of the three bags must be less than or equal to1414 kg.
Hence, the inequality can be written as:
S+M+LS+M+L
≤≤
1414
Next, make sure that only nn is on the left side
SS++MM++LL
≤≤
1414
ss++s+1s+1++s+4s+4
≤≤
1414
Substitute the known values
3s+53s+5
≤≤
1414
Combine like terms
3s+53s+5-5−5
≤≤
1414-5−5
Subtract 55 from both sides
3s3s÷3÷3
≤≤
99÷3÷3
Divide both sides by 33
ss
≤≤
33
s≤3s≤3
Question 5 of 5
5. Question
Jack is flying an air balloon at an altitude of 1600016000 feet and is experiencing some bad weather. For him to fly safely, Jack needs to increase his altitude to at least 1700017000 feet or decrease his altitude to no more than 1300013000 feet. Form an inequality.
The number lines below are scaled as 1:10001:1000ft