In math questions answers each questions are solved with explanation. The questions are based from different topics. Care has been taken to solve the questions in such a way that students can understand each and every step.
1. Which is greater than 4?
(a) 5,
(b) -5,
(c) -1/2,
(d) -25.
Solution:
5 greater than 4.
Answer: (a)
2. Which is the smallest?
(a) -1,
(b) -1/2,
(c) 0,
(d) 3.
Solution:
The smallest number is -1.
Answer: (a)
3. Combine terms: 12a + 26b -4b – 16a.
(a) 4a + 22b,
(b) -28a + 30b,
(c) -4a + 22b,
(d) 28a + 30b.
Solution:
12a + 26b -4b – 16a.
= 12a – 16a + 26b – 4b.
= -4a + 22b.
Answer: (c)
4. Simplify: (4 – 5) – (13 – 18 + 2).
(a) -1,
(b) –2,
(c) 1,
(d) 2.
Solution:
(4 – 5) – (13 – 18 + 2).
= -1-(13+2-18).
= -1-(15-18).
= -1-(-3).
= -1+3.
= 2.
Answer: (d)
5. What is |-26|?
(a) -26,
(b) 26,
(c) 0,
(d) 1
Solution:
|-26|
= 26.
Answer: (b)
Solution:
3y(x – 3) -2(x – 3).
= (x – 3)(3y – 2).
Answer: (c).
9. Solve for x: 2x – y = (3/4)x + 6.
(a) (y + 6)/5,
(b) 4(y + 6)/5,
(c) (y + 6),
(d) 4(y - 6)/5.
Solution:
2x – y = (3/4)x + 6.
or, 2x - (3/4)x = y + 6.
or, (8x -3x)/4 = y + 6.
or, 5x/4 = y + 6.
or, 5x = 4(y + 6).
or, 5x = 4y + 24.
or, x = (4y + 24)/5.
Therefore, x = 4(y + 6)/5.
Answer: (b).
11. Find the value of 3 + 2 • (8 – 3)
(a) 25,
(b) 13,
(c) 17,
(d) 24,
(e) 15.
Solution:
3 + 2 • (8 – 3)
= 3 + 2 (5)
= 3 + 2 × 5
= 3 + 10
= 13
Answer: (d)
15. What is the radius of a circle that has a circumference of 3.14 meters?
Solution:
Circumference of a circle = 2πr.
Given, circumference = 3.14 meters.
Therefore,
2πr = Circumference of a circle
or, 2πr = 3.14.
or, 2 × 3.14r = 3.14,[Putting the value of pi (π) = 3.14].
or, 6.28r = 3.14.
or, r = 3.14/6.28.
or, r = 0.5.
Answer: 0.5 meter.
16. The trip from Carville to Planesborough takes 4\(\frac{1}{2}\) hours when travelling at a constant speed of 70 miles per hour. How long, in hours, does the trip take when travelling at a constant speed of 60 miles per hour.
Solution:
Distance = Speed × Time
Distance form Carville to Planesborough = 70 × 4\(\frac{1}{2}\) miles
= 70 × \(\frac{9}{2}\) miles
= 315 miles
Now travelling the same distance (315 miles) at a constant speed of 60 miles per hour.
Time = \(\frac{Distance}{Speed}\)
= \(\frac{315}{60}\) hours
= 5.25 hours
Time taken to travel Carville to Planesborough a constant speed of 60 miles per hour = 5.25 hours.
17. The table below shows the number of hours Simon worked this week at his job. Days: Hours: Monday 6 2/3. Tuesday 4 1/2. Thursday 7 1/4. He earns $12 an hour at his job. How much will Simon get paid for the hours he worked this week?
Solution:
Total hours Simon worked this week = 6 2/3 + 4 1/2 + 7 1/4
= \(\frac{20}{3}\) + \(\frac{9}{2}\) + \(\frac{29}{4}\) hours
= \(\frac{80}{12}\) + \(\frac{54}{12}\) + \(\frac{87}{12}\) hours
= \(\frac{80 + 54 + 87}{12}\) hours
= \(\frac{221}{12}\) hours
He earns $12 an hour at his job.
Simon get paid for the hours he worked this week = $ \(\frac{221}{12}\) × 12 = $ 221
18. Carlos is looking to buy a house where the floor plan shows the ratio of the area of the living room to the kitchen to the bedroom is 5 : 3 : 4. If the combined area of those three rooms is 360 square feet, how much larger, in square feet, is the living room than the bedroom?
Answer:
The area of the living room = \(\frac{5}{5 + 3 + 4}\) × 360 square feet
= \(\frac{5}{12}\) × 360 square feet
= 5 × 30 square feet
= 150 square feet
The area of the bed room = \(\frac{4}{5 + 3 + 4}\) × 360 square feet
= \(\frac{4}{12}\) × 360 square feet
= 4 × 30 square feet
= 120 square feet
Therefore, living room is (150 - 120) square feet = 30 square feet larger than the bed room.
19. Frank runs a business called Frank’s Fresh Farm Produce. Once a week he drives to farms where he buys the best possible fresh produce for his customers. Frank can travel 600 miles on a full tank of gas. Usually Frank has time to visit only one farm on each trip, but one week he decides to visit both Stan’s and Louisa’s farms.
● When Frank drives from his store to Stan’s farm and back, he knows he uses 5/12 of a tank
● When Frank drives to Louisa’s farm and back, he uses 1/3 of a tank.
From a map of the area, he learns that there is a road from Stan’s farm to Louisa’s farm that is 120 miles long. He realizes that he can drive from his store to Stan’s farm, then to Louisa’s farm, and then back to his store on a loop. Frank can tell by looking at his fuel gauge that he has 5/8 of a tank of gas. Can he drive this loop without having to stop for fuel? Or should he buy gas before he starts his trip?
Solution:
Frank drives from his store to Stan’s farm and back, he knows he uses 5/12 of a tank
Frank can travel 600 miles on a full tank of gas.
So, for 5/12 tank of gas he can travel = 600 × 5/12 = 50 × 5 = 250 mi
Therefore, the distance from store to Stan’s farms = 250/2 mi = 125 mi
Similarly, when Frank drives to Louisa’s farm and back, he uses 1/3 of a tank.
So, for 1/3 tank of gas tank he can travel = 600 × 1/3 = 200 × 1 = 200 mi
Therefore, the distance from store to Stan’s farms = 200/2 mi = 100 mi
Distance from Stan’s farm to Louisa’s farm is 120 mi.
Loop distance = Store to Stan’s farm to Louisa’s farm to Store
= 125 mi + 120 mi + 100 mi
= 345 mi
Therefore, Loop distance = 345 mi
Frank can tell by looking at his fuel gauge that he has 5/8 of a tank of gas.
So, for 5/8 tank of gas tank he can travel = 600 × 5/8 = 75 × 5 = 375 mi
Therefore, 5/8 tank of gas tank Frank can travel = 375 mi
345 mi < 375 mi
Thus, Frank drive this loop without having to stop for fuel.
20. A moving company charges a $200 fee, plus $4 for every item that is delivered safely. The moving company takes $5 off the bill for every item that is lost or broken.
A florist hired this moving company to move 578 clay pots. The moving company lost 6 pots, broke 12 pots, and delivered the rest of the pots safely. How much did the florist pay the moving company?
A. $2,350
B. $2,440
C. $2,442
D. $2,512
Answer:
A. $2,350
The company lost 6 pots and broke 12 pots.
Total number of lost and broken pots = 6 + 12 = 18
Company takes $5 off the bill for every item that is lost or broken.
The company takes 18 × 5 = $ 90 off the bill for 18 lost and broken pots.
Florist hired this company to move 578 clay pots.
We know, total number of lost and broken pots = 18
Therefore, total number of safely delivered pots = (578 - 18) pots = 560 pots.
Company charges a flat fee of $200, plus $4 for every item that is delivered safely.
So, for 560 pots the company charges $200 + $(560 × 4) = $200 + $2240 = $2440.
We know, the company takes $90 off the bill for 18 lost and broken pots.
Therefore, the florist paid $2440 - $90 = $2350 to the moving company.
21. Charlie and Augustus guessed the weight of a bar of chocolate and decided the person whose guess was closest would get to eat it. Charlie guessed 35 grams, Augustus guessed 40 grams, and the actual weight was 37.5 grams. Augustus says he should get the chocolate bar and showed this work below. Do you agree with Augustus? Explain below with mathematical and written reasoning.
22. Two out of three balls in a Multi-colored package are pink. How many balls in a package of 21 will be pink?
Solution:
Let the x out of 21 balls are pink.
2 out of 3 balls in a Multi-colored package are pink.
x : 2 = 3 : 21
x/2 = 21/3
3x = 2 × 21
3x = 42
x = 42/3 = 14
Answer: There are 14 pink balls.
23. Carmen wants to buy a snack that costs $3.74 including tax. Carmen gives the cashier $10. Which equation can be used to find the amount of change, x, that Carmen receives? How much change did she receive?
(a) x + 3.74 = 10; Carmen receives $6.26 in change.
(b) x + 10 = 3.74; Carmen receives $13.74 in change.
(c) x - 3.74 = 10; Carmen receives $13.74 in change.
(d) x - 10 = 3.74; Carmen receives $6.26 in change.
Answer:
(a) x + 3.74 = 10; Carmen receives $6.26 in change.
24. Melissa earns $5 an hour for babysitting. If she babysat for 7 hours on Saturday and 6 hours on Sunday, how much money did she make in total?
Solution:
Melissa earns $5 an hour for babysitting.
Total work hours on Saturday and Sunday = (7 + 6) hours = 13 hours
She earn = $ 5 × 13 = $ 65
Answer: $ 65
25. Kiran and Clare live 24 miles away from each other along a trail. One Saturday the two friends statred walking towards each other along the trail at 8:00 am with a plan ot have a picnic when they met. Kiran walks at a speed of 3 miles per hour while Clrare walks 3.4 miles per hour. after one hour, how far apart will they be?
Solution:
Kiran and Clare live 24 miles away from each other along a trail.
Kiran walks at a speed of 3 miles per hour
In 1 hour Kiran covered 3 miles
Clrare walks 3.4 miles per hour.
In 1 hour Clrare covered 3.4 miles
In 1 hour both Kiran and Clrare covered = (3 + 3.4) miles= 6.4 miles.
(They statred walking towards each other along the trail, so we add the distance)
After one hour they will be (24 - 6.4) miles = 17.6 miles apart.
Answer: 17.6 miles
26. 8/9 kilogram of berries is added to a container that already has \(\frac{7}{3}\) kilograms of berries. After this, the container is \(\frac{2}{3}\) of the way full. How many kilograms of berries can this container hold?
Solution:
\(\frac{8}{9}\)kilogram of berries is added to a container that already has 7/3 kilograms of berries.
\(\frac{8}{9}\) + \(\frac{7}{3}\) = \(\frac{24}{27}\) + \(\frac{63}{27}\) = \(\frac{87}{27}\) = \(\frac{29}{9}\) kilograms
\(\frac{2}{3}\) of the way full = \(\frac{29}{9}\) kilograms
Container hold = \(\frac{29}{9}\) ÷ \(\frac{2}{3}\) kilograms
= \(\frac{29}{9}\) × \(\frac{3}{2}\) kilograms
= \(\frac{87}{18}\) kilograms
= \(\frac{29}{6}\) kilograms
= 4\(\frac{5}{6}\) kilograms
Answer: 4\(\frac{5}{6}\) kg
27. Shylah is picking out a rectangular aquarium for her new fish. The height of aquarium A is half the height of aquarium B. The length of aquarium B is twice the length of aquarium A. The widths of the two aquariums are the same.
Shylah wants to buy the aquarium with the greater amount of room for her fish to swim.
Which aquarium should she buy? Explain your reasoning.
Solution:
The height of aquarium A is half the height of aquarium B.
Let the height of aquarium B = H
The height of aquarium A = H/2
The length of aquarium B is twice the length of aquarium A.
Let the length of aquarium A = L
The length of aquarium B = 2L
The widths of the two aquariums are the same.
Let widths of the two aquariums = W
Volume of aquarium A = Length × Width × Height
= L × W × H/2
= 1/2 (L × W × H)
Volume of aquarium B = Length × Width × Height
= 2L × W × H
= 2 (L × W × H)
Volume of aquarium B > Volume of aquarium A
Shylah should buy Aquarium B
Answer: Aquarium B
28. At a bus station, buses begin their routes at 6:00 a.m. The schedule for two of the buses is based on the time intervals listed below.
Bus A has a long route and leaves the station every 75 minutes.
Bus B has a short route and leaves the station every 15 minutes.
What is the next time Bus A and Bus B will leave the bus station at the same time?
Solution:
The LCM (least common multiple) of 75 and 15 is 75.
Now add 75 minutes to 6:00 a.m.
75 minutes = 1 hour 15 minutes
6:00 a.m. + 1 hour 15 minutes = 7:15 a.m.
At 7:15 a.m. bus A and bus B will leave the bus station at the same time.
29. After Winter Break, 6 musicians joined the drama club so the number of actors in the club was equal to the number of musicians in the club. How many more musicians need to join the club to make the ratio of actors to musicians 3 to 5?
A. 6 musicians
B. 9 musicians
C. 10 musicians
D. 16 musicians
Solution:
At the start of the school year,
Let the number of members = x
Actors : Musicians = 5 : 3
Number of actors = \(\frac{5}{8}\)x and number of musicians = \(\frac{3}{8}\)x
After Winter Break, 6 musicians joined the drama club.
Number of musicians after winter break = \(\frac{3}{8}\)x + 6
The number of actors in the club was equal to the number of musicians in the club.
According to the problem,
\(\frac{5}{8}\)x = \(\frac{3}{8}\)x + 6
\(\frac{5}{8}\)x - \(\frac{3}{8}\)x = 6
\(\frac{2}{8}\)x = 6
x = 6 × \(\frac{8}{2}\)
x = \(\frac{48}{2}\)
x = 24
At the start of the school year, the number of members = 24
Number of actors = \(\frac{5}{8}\) × 24 = 15
Number of musicians = \(\frac{3}{8}\) × 24 = 9
After Winter Break, 6 musicians joined the drama club.
Number of actors = Number of musicians = 15
Let y number of musicians need to join the club to make the ratio of actors to musicians 3 to 5
Therefore,
15 : (15 + y) = 3 : 5
\(\frac{15}{15 + y}\) = \(\frac{3}{5}\)
3 × (15 + y) = 15 × 5
45 + 3y = 75
3y = 75 - 45
3y = 30
y = \(\frac{30}{3}\)
y = 10
Thus, 10 number of musicians need to join the club to make the ratio of actors to musicians 3 to 5
Answer:
C. 10 musicians
30. LaRon is shelving books in a library. He has 36 mysteries, 27 biographies, and 45 historical fiction books. LaRon wants to put the same number of books on each shelf, and he will only put books of the same genre on the same shelf.
What is the smallest possible number of shelves LaRon would need to store these books in this way?
Solution:
Mysteries = 36
Biographies = 27
Historical = 45
Now find the factors of 36, 27 and 45
The factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18 and 36.
The factors of 27 = 1, 3, 9, and 27.
Factors of 45 = 1, 3, 5, 9, 15 and 45.
The highest common factor of 36, 27 and 45 is 9.
Hence, the minimum number of book in each shelf = 9
Answer: 9
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