August 9, 2020

Chapters

- Exercise 1
- Exercise 2
- Exercise 3
- Exercise 4
- Exercise 5
- Exercise 6
- Exercise 7
- Exercise 8
- Exercise 9
- Exercise 10
- Exercise 11
- Solution of exercise 1
- Solution of exercise 2
- Solution of exercise 3
- Solution of exercise 4
- Solution of exercise 5
- Solution of exercise 6
- Solution of exercise 7
- Solution of exercise 8
- Solution of exercise 9
- Solution of exercise 10
- Solution of exercise 11

## Exercise 1

At a community meeting, there are double the number of women than men and triple the number of children than the total of men and women combined. How many men, women, and children are there if people attend the meeting?

## Exercise 2

A barrel of oil has of its content removed. Then, it is filled with liters and the total content is the capacity of the barrel. Calculate the total capacity of the barrel.

## Exercise 3

A farm has pigs and turkeys. In total, there are heads and paws. How many pigs and turkeys are there on the farm?

## Exercise 4

Peter went on a road trip, during which time liters of gasoline were consumed. However, he completed the trip in two stages. In the first, he consumed of the gasoline that was in the tank and in the second stage, half of the gasoline that he had left in the tank.

1. Determine the number of liters of gasoline that were in the tank before the trip.

2. Determine the number of liters consumed at each stage.

## Exercise 5

In a bookstore, Anne buys a novel with a third of her money and a comic with two-thirds of what remained. When she left the bookstore, she had dollars. How much money did Anne have before arriving at the store?

## Exercise 6

A clock sounds to indicate the time of 3 o'clock. At what time between and will the hour and minute needles overlap?

## Exercise 7

A clock sounds to indicate the time of 2 o'clock. At what time will its needles form a right angle for the first time?

## Exercise 8

A truck leaves a city at a speed of mph. An hour later, a car leaves the same city and travels in the same direction at a speed of mph.

1. How many hours after leaving the city will the car reach the truck?

2. What is the distance from the city where the car will reach the truck?

## Exercise 9

At 9 a.m., two cyclists simultaneously leave their houses and travel towards each other on the same road. Houses A and B are located miles away from each other. If the cyclist who leaves from House A pedals at a constant speed of mph, and the cyclist who leaves from House B travels at mph, how far from House A will the two meet and at what time?

## Exercise 10

A faucet takes hours to fill a water tank, and another faucet takes four hours to fill a tank of the same size. How long will it take to fill a tank of the same size if both faucets are distributing water together into the same tank?

## Exercise 11

A golden brick of purity weighs grams. What amount of pure copper should be added to lower its purity to ?

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## Solution of exercise 1

At a community meeting, there are **double the number of women than men** and **triple the number of children than the total number of men and women combined**. How many men, women, and children are there if **people** attend the meeting?

Men:

Women:

Children:

Men:

Women: =

Children: =

## Solution of exercise 2

A barrel of oil has of its content removed. Then, it is filled with liters and the total content is the capacity of the barrel. Calculate the total capacity of the barrel.

Let the total volume of the barrel equal to "x".

The first step is to deduct the from the total amount.

The next step is to add the liters which will equal to

After talking LCM:

## Solution of exercise 3

A farm has pigs and turkeys. In total, there are heads and paws. How many pigs and turkeys are there on the farm?

Let the number of pigs =

Turkeys =

Pigs =

Turkeys =

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## Solution of exercise 4

Peter went on a road trip, during which time liters of gasoline were consumed. However, he completed the trip in two stages. In the first, he consumed of the gasoline that was in the tank and in the second stage, half of the gasoline that he had left in the tank.

1. Determine the number of liters of gasoline that were in the tank before the trip.

First stage.

Second stage.

2. Determine the number of liters consumed at each stage.

First stage:

Second stage:

## Solution of exercise 5

In a bookstore, Anne buys a novel with a third of her money and a comic with two-thirds of what remained. When she left the bookstore, she had dollars. How much money did Anne have before arriving at the store?

Let the total amount that Anne had equal to "x"

Cost of novel =

Cost of comic =

The remainder cost =

dollars

## Solution of exercise 6

A clock sounds to indicate the time of 3 o'clock. At what time between and will the hour and minute needles overlap?

Keep in mind that the angle or arc representing the minute hand's position is always times greater than the arc that describes the hour hand.

x is the arch that describes the needle hourly.

is the arch that describes the minute hand.

The needles will overlap at and seconds.

## Solution of exercise 7

A clock sounds to indicate the time of 2 o'clock. At what time will its needles form a right angle for the first time?

Turning clockwise, the needles will form a right angle approximately at . Therefore, let x be the arc that describes the hour needle.

**x is the arc that describes the hour needle.**

**, is the arc that describes the minute hand.**

The clock will form a angle at and seconds.

## Solution of exercise 8

A truck leaves a city at a speed of mph. An hour later, a car leaves the same city and travels in the same direction at a speed of mph.

1. How many hours after leaving the city will the car reach the truck?

Distance traveled by car =

Distance traveled by truck =

As the car leaves the city one hour later than the truck, the time it will take to reach the truck will be hours.

2. What is the distance from the city where the car will reach the truck?

miles

## Solution of exercise 9

At 9 a.m., two cyclists simultaneously leave their houses and travel towards each other on the same road. Houses A and B are located miles away from each other. If the cyclist who leaves from House A pedals at a constant speed of mph, and the cyclist who leaves from House B travels at mph, how far from House A will the two meet and at what time?

The cyclist travels at mph from house A and his friend travels at mph from house B. They will meet up at a certain place and we will call that place C. If we add the distance of AC and CB, we know that their sum will be (because that is the overall distance). To find those distances, we will use speed formula since we know the speed and we will assume that at "t", they will meet each other.

Distance traveled by the cyclist from house A =

Distance traveled by the cyclist from house B =

hours

Let's convert hours into hour:min

minutes

time = hour and minutes

They will meet at 11:36 am.

miles

## Solution of exercise 10

A faucet takes hours to fill a water tank, and another faucet takes four hours to fill a tank of the same size. How long will it take to fill a tank of the same size if both faucets are distributing water together into the same tank?

In one hour the first faucet fills of the tank.

In one hour the second faucet fills of the tank.

In one hour two together faucets will have filled:

hours

## Solution of exercise 11

A golden brick of purity weighs grams. What amount of pure copper should be added to lower its purity to ?

Gold | Copper | Total | |
---|---|---|---|

No. of g | |||

Pure Gold |

Copper grams

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