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 cm3 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.
1. Answer :
322 miles/11.5 gallons = 28 miles/gallon
The car's gas mileage is 28 miles per gallon.
2. Answer :
Density = Mass/Volume
= 483 grams/46 cm3
= 10.5 grams/cm3
The density of silver is 10.5 grams per cubic centimeter.
3. Answer :
From the ratio 1 : 2 : 3, the three angles are
x, 2x, 3x
In any triangle, sum of the angles is equal to 180°.
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°
4. Answer :
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
5. Answer :
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
6. Answer :
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
42x2 = 378
42x2 = 378
Divide each side by 42.
x2 = 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.
7. Answer :
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.
8. Answer :
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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