1. Vishal purchased 15 plants at a nursery, some at $3 and the rest at $5. The total cost was $55. How many $5 plants did he buy?
2. Given that x < 5, rewrite 5x - l x – 5 l without using absolute value signs.
3. Northwestern Middle School sells graphing calculators to raise funds. The school pays $90 for each calculator and sells them for $100 apiece. They hope to earn enough money to purchase an additional set of 30 calculators. How many calculators must they sell to reach their goal?
4. Simran defined a clever integer as an even integer that is greater than 20, less than 120, and such that the sum of its digits is 9. What fraction of all clever integers is divisible by 27? Express your answer as a common fraction.
5. If a 12 pandas can eat 5 shoots of bamboo in 7 days, how long would it take a group of 7 pandas to eat 37 shoots of bamboo? Express your answer as a common fraction.
Participants with the most correct answers/best efforts will have their name printed in a problem!
HAPPY PROBLEM SOLVING!
1. 5 plants
ReplyDelete2. 4x-5<15 not so sure about this one
3. 270 calculators
4. 3/5
5. still thinking
5. 63 3/7
ReplyDeleteGrace, well done! Problem 2 was missing the abosolute value signs, but I just added them in. Check over your work for problems 4 and 5 again.
ReplyDelete1.5
ReplyDelete2.4x-5<12
3.270
4.2/5
5.88 4/5
1) 5 plants were bought at $5
ReplyDelete2) 4x-5<5
3) 270 calculators
4) 2/5
5) Working on it.
Answer to 2nd problem is 6x - 5
ReplyDeleteGreat job, everyone! I will comment on your answers after I recieve a few more responses.
ReplyDeleteI'm posting a new question on the marathon. Go ahead and try that. Have fun!
1) 5 plants
ReplyDelete2) 4x-5<5
3) 27 calculators
4) 1/12
1) 5
ReplyDelete2) 4x-5<5
3) 270
4) Still working...
5) 51 and 4/5 days
4. 2/5. Careless mistake.
ReplyDelete2. 6x-5
5. stumped
I got a different answer for 5. It is 444/5 or 88 4/5.
ReplyDeleteNeha and Simran, could you please post your approach/solution to problem 5? Thanks!
ReplyDeleteGrace, please post your problem for the marathon run.
You guys are doing an AWESOME job!
A new marathon problem is posted. Take a look at it and have fun working it out!
ReplyDelete1) 5 bags
ReplyDelete2) 4x-5<15
3) 90 x 30 = 2700/100 = 27 calculators
4) 1/12
5) no idea
Vishal, try problems 2 through 5 with the following hints until I post the solutions.
ReplyDeleteProblem 2: The first step is to negate |x - 5|.
Problem 3: How many dollars in profit does Northwestern make on each calculator? How much will it cost to buy 30 additional calculators if the school makes $___ on each calculator they sell?
Problem 4: Make a list of all the clever integers. How many fit the criteria? Remember that probability = success/total.
Problem 5: Make 3 columns - pandas, shoots, and days. Then, fill in the chart step by step. We already know that 12 pandas eat 5 shoots of bamboo in 7 days, so it must mean that 12 pandas eat 37 shoots of bamboo in 259/5 days. This way, I've got the "shoots variable" out of the way. Finish the table in this manner.
Also, please post your solution to the marathon problem, not just your answer. Thanks!
2)6x-5
ReplyDelete3)270 calculators
4)2/5
5)73 days
Good job, Vishal! Looks like the hints helped you do problems 2, 3, and 4! Keep trying the 5th one.
ReplyDeleteSolutions
ReplyDelete1. x is 3 dollar plants, y is 5 dollar plants.
x + y = 15
3x + 5y = 55
From the first, x = 15 – y
Put that into the second, 3(15 – y) + 5y = 55
45 – 3y + 5y = 55
2y = 10
y = 5
2. If x < 5 then we have x – 5 < 0 and our term is 5x – (5 – x) = 5x – 5 + x = 6x – 5.
3. They make $10 profit on each calculator sold since $100 - $90 = $10 so they need to sell 2700/10 = 270 calculators.
4. It is divisible by 9 and is even. 36, 54, 72, 90, 108 work. There are 2 that are divisible by 27, so 2/5.
5. The number of shoots of bamboo is directly proportional to the number of pandas and the amount of days. We have:
[(Number of pandas) × (Number of days)] ÷ (Number of shoots of bamboo)
Inserting their numerical value, we have (12 × 7) ÷ 5 = 84/5. We want to know how long it will take 7 pandas to eat 37 shoots of bamboo. Inserting the variables, we have:
(7x)/37 = 84/5
Solving, we have:
35x = 3108
x = 444/5 days
I just used the unitary method for number 5
ReplyDeleteI used the unitary method, too! But I also used a easy formula(for me)--- work = rate x time.
ReplyDeleteThis comment has been removed by the author.
ReplyDelete1. 5 $5 plants
ReplyDelete2. 6x-5
3. 270 calculators
4. 2/5
5. 444/5