**Problem 1 :**

A car travels 322 miles on 11.5 gallons of gas. What is the car’s gas mileage ?

**Problem 2 :**

A volume of 46 cm^{3} of silver has a mass of 483 grams. What is the density of silver ?

**Problem 3 :**

If the angles of a triangle are in the ratio of 1 : 2 : 3, then find the measure of each angle.

**Problem 4 :**

The sum of two numbers is 14 and the ratio of the two numbers is -3. What is the product of the two numbers ?

**Problem 5 :**

Let 5(x + y) = 7y. Find the ratio between x and y.

**Problem 6 :**

The length and width of a rectangular garden are in the ratio 6 : 7. If the area of the garden is 378 square meters, find perimeter of the garden.

**Problem 7 :**

Mr. John can travel 218.5 miles of distance on consumption of 9.5 gallons of gas. How many miles can he travel on 15.5 gallons of gas ?

**Problem 8 :**

The ratio between the speeds of two cars is 7 : 8. If the second car runs 400 miles in 5 hours, then find the speed of the first car.

**Problem 1 :**

A car travels 322 miles on 11.5 gallons of gas. What is the car’s gas mileage ?

**Solution :**

322 miles / 11.5 gallons = 28 miles / gallon

The car's gas mileage is 28 miles per gallon.

**Problem 2 :**

A volume of 46 cm^{3} of silver has a mass of 483 grams. What is the density of silver ?

**Solution : **

Density = Mass / Volume

Density = 483 grams / 46 cm^{3}

Density = 10.5 grams / cm^{3}

The density of silver is 10.5 grams per cubic centimeter.

**Problem 3 :**

If the angles of a triangle are in the ratio of 1 : 2 : 3, then find the measure of each angle.

**Solution :**

From the ratio 1 : 2 : 3, the three angles are

x, 2x, 3x

In any triangle, sum of the angles is equal to 180°.

Then,

x + 2x + 3x = 180°

6x = 180

Divide each side by 6.

x = 30

Measure of each angle :

First angle = 30°

Second angle = 2(30) = 60°

Third angle = 3(30) = 90°

**Problem 4 :**

The sum of two numbers is 14 and the ratio of the two numbers is -3. What is the product of the two numbers ?

**Solution : **

Let x and y be the numbers.

The sum of two numbers is 14.

x + y = 14 -----(1)

Ratio of the two numbers is -3.

x/y = -3

Multiply each side by y.

x = -3y -----(2)

Substitute -3y for x in (1).

-3y + y = 14

-2y = 14

Divide each side by -2.

y = -7

Substitute -7 for y in (2).

x = -3(-7)

x = 21

So,, the two numbers are 21 and -7.

Product of the two numbers :

= 21(-7)

= -147

**Problem 5 :**

Let 5(x + y) = 7y. Find the ratio between x and y.

**Solution : **

5(x + y) = 7y

5x + 5y = 7y

Subtract 5y to each side.

5x = 2y

Divide each side by 5y.

5x/5y = 2y/5y

x/y = 2/5

x : y = 2 : 5

**Problem 6 :**

The length and width of a rectangular garden are in the ratio 6 : 7. If the area of the garden is 378 square meters, find perimeter of the garden.

**Solution : **

From the ratio 6 : 7,

length = 6x

width = 7x

Given : Area of the rectangle is 378 square meters.

l ⋅ w = 378

Substitute.

6x ⋅ 7x = 378

42x^{2} = 378

42x^{2} = 378

Divide each side by 42.

x^{2} = 9

Take square root on both sides.

x = 3

Find the length and width :

length = 6(3) = 18 meters

width = 7(3) = 21 meters

Perimeter of the rectangle :

= 2l + 2w

Substitute.

= 2(18) + 2(21)

= 36 + 42

= 78

The perimeter of the garden is 78 meters.

**Problem 7 :**

Mr. John can travel 218.5 miles of distance on consumption of 9.5 gallons of gas. How many miles can he travel on 15.5 gallons of gas ?

**Solution : **

Distance covered on 9.5 gallons of gas = 218.5 miles

Distance covered on 1 gallon of gas :

= 218.5 / 9.5

= 23 miles

Distance covered on 15.5 gallons of gas :

= 15.5 ⋅ 23

= 356.5 miles

Mr. John can travel 356.5 miles on 15.5 gallons of gas.

**Problem 8 :**

The ratio between the speeds of two cars is 7 : 8. If the second car runs 400 miles in 5 hours, then find the speed of the first car.

**Solution : **

From the ratio 7 : 8,

speed of the first car = 7x

speed of the second car = 8x

Given : The second car runs 400 miles in 5 hours.

Time = Distance / Speed

Substitute.

5 = 400 / 8x

5 = 50 / x

Multiply each side by x.

5x = 50

Divide each side by 5.

x = 10

Speed of the first car :

= 7(10)

= 70 miles per hour

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