Savatingiz boʻsh
Answer the question
Good day, Old Lady! How many \latex{ miles } is there to the glass mountain?
Lucky for you, you showed some respect.
After solving an exercise, read the question one more time and then answer it. Sometimes, solving the most difficult part of a problem does not answer the question of the exercise.
Example 1
Anna swam the same number of laps in a \latex{ 25-meter } pool as Carl did in a \latex{ 50-meter } pool. They swam a total of \latex{ 6 \;km } together. How many times more did Carl swim than Anna?
Ben, Eric, and Zoe solved the word problem. Read their solutions and decide whose answer is correct.
Solution
Ben’s solution:
Anna's one lap
Carl's one lap
\latex{ 25 \,m }
\latex{ 50 \,m }
The sum of one of Carl's laps and one of Anna's laps is \latex{ 25 + 50 = 75\; m }. The total distance the two of them swam is \latex{ 6 \;km = 6,000 \;m }, which is equal to \latex{ 6,000 ÷ 75 = 80 } laps. Therefore, Anna swam \latex{ 80 × 25 = 2,000 \;metres }, and Carl swam \latex{ 80 × 50 = 4,000 \;metres }.
Check: \latex{4,000 + 2,000 = 6, 000\, m} \latex{= 6\,km}.
Eric’s solution:
Anna and Carl swam the same number of laps, so they both swam \latex{ 6 ÷ 2 = 3 \;kilometres }.
Zoe’s solution:
Since Carl swam the same number of laps as Anna, but in a pool twice as long as hers, he swam twice as much as Anna.
Evaluate the solutions. Which one is correct and which one is not? Why?
Ben's solution is incomplete. Although he correctly calculated that Anna swam\latex{ 2,000 \;metres} and Carl swam \latex{ 4,000 \;metres}, this did not answer the question. He should have included the fact that Carl swam \latex{ 4,000 ÷ 2,000 = 2 } times as much as Anna.
Eric's solution is incorrect. Although Anna and Carl swam the same number of laps, the two pools had different lengths; thus, they could not swim the same number of \latex{ kilometres. }
Zoe's solution is correct. Although she did not calculate how many \latex{ metres } each of them swam, she was able to answer the question. This is because the information that Anna and Carl swam a total of \latex{ 6 \;km } together is irrelevant, and the question can be answered without it.
Example 2
There are five rooms on the first floor of a hotel, which are either triple or quadruple rooms. How many people are staying in triple rooms if all \latex{ 18 } places on the floor are occupied?
Solution 1
Draw the five rooms with three beds in each of them.
So far, \latex{ 5 × 3 = 15 } beds have been drawn. Thus, you have to complete the diagram with \latex{ 18 -15 = 3 } more beds. Consequently, there are three quadruple rooms, and \latex{ 5 - 3 = 2 } triple rooms on the floor.
Check:
There are three quadruple rooms, equipped with \latex{ 3 × 4 = 12 } beds.
There are two triple rooms, equipped with \latex{ 2 × 3 = 6 } beds.
There are two triple rooms, equipped with \latex{ 2 × 3 = 6 } beds.
Answer:
Six people stay in triple rooms on the first floor of the hotel.
Solution 2
If all five rooms were quadruples, there would be \latex{ 5 × 4 = 20 } beds on the first floor. As there are two fewer places, there are only two triple rooms, each equipped with three beds. Therefore, there are two triple and three quadruple rooms on the floor.
Answer:
Six people stay in triple rooms on the first floor of the hotel.
Exercises
{{exercise_number}}. A new highway is being built. So far, \latex{ 354 \;kilometres } have been constructed. The remaining section that is still under construction is one-sixth the length of the completed section.
What fraction of the length of the entire highway is still under construction?
{{exercise_number}}. John has chickens and rabbits on his farm. The animals have a total of \latex{ 48 } legs and \latex{ 18 } heads. How many rabbits and how many chickens does John have?
{{exercise_number}}. The police are following the tricycle thieves on bicycles. They are rolling on \latex{ 34 } wheels and steering \latex{ 14 } handlebars altogether. How many tricycles were stolen?
{{exercise_number}}. A magic cape with a hat costs \latex{ 3,000 \;coins }. The price of the cape is eight-sevenths of that of the hat. How much more does the cape cost than the hat?
{{exercise_number}}. Dora and Kate wanted to share some stickers equally. When they counted the number of stickers they had, they realised that Dora had \latex{ 28 } more than Kate. Dora then gave some stickers to Kate, and ended up with four fewer stickers than Kate. Based on this, can you determine how many stickers Dora gave to Kate and the total number of stickers they had?
{{exercise_number}}. A group of \latex{ 35 } explorers is travelling through the Sahara. The expedition includes horses, Bactrian camels, and people. Each horse and camel is ridden by one person. Five people are walking, which is exactly one-third of the number of camels. How many feet are walking in the desert?
{{exercise_number}}. Ben is building a tower using cubes with \latex{ 40 \;mm }-long edges. He stacks the cubes so that their faces overlay each other. If he puts two more cubes at the top of the tower, by how many \latex{ square } \latex{ centimetres } does the surface area of the tower increase?
{{exercise_number}}. Zoe is reading a book. On Saturday, she read one-fourth of the book. On Sunday, she read \latex{ 22 } pages more than on Saturday. On Wednesday, she read half as much as she did on Tuesday. She wanted to finish the book on Thursday because only one-tenth of the book was left; however, she could only read \latex{ 17 } pages as she had to study for her English test. On Friday, she read the remaining \latex{ 25 } pages of the book. How many pages is the book?
{{exercise_number}}. Anna's phone bill includes two types of charges: a monthly subscription fee and a minute fee for each call. Her minute fee was twice as much in September and three times as much in October as in August. If her phone bill was €\latex{25} in August and €\latex{45} in September, how much did she pay in October?
Quiz
I paid a €\latex{ 12 } deposit for a book. Now, I still have to pay the amount that I would need to pay if I had paid the amount that I still have to pay. How much does the book cost?
