Problem 1 :
Carter's SUV requires 8 gallons of gasoline to travel 148 miles. How many gasoline, to the nearest gallon, will he need for 500 mile trip?
Solution :
Let x be the quantity of gasoline in gallons.
8 : 148 = x : 500
Product of extremes = Product of means
8 ⋅ 500 = 148 ⋅ x
x = (8 ⋅ 500)/148
x = 27.02
So, Carter needs 27.02 gallons of gasoline for a 500 mile trip.
Problem 2 :
On a map 1 inch represents 5 miles. If a certain state is represented on a map by the rectangle 10 inches by 7.2 inches. What is the area of the state in square miles ?
Solution :
length of rectangle = x and width of the rectangle = y
1 : 5 = 10 : x 1 ⋅ x = 5 ⋅ 10 x = 50 |
1 : 5 = 7.2 : y 1 ⋅ y = 7.2 ⋅ 5 y = 36 |
Area of rectangle = 50(36)
= 1800 square miles
Problem 3 :
Together there are 754 students and teachers in the meeting. If the ratio of students to teachers is 27 : 2, how many teachers are there ?
Solution :
Total number of students and teachers = 754
number of students = 27x
number of teachers = 2x
27x + 2x = 754
29x = 754
x = 754/29
x = 26
Problem 4 :
Concrete is made by mixing cement, sand and gravel in the ratio 5 : 9 : 13. How much cement is needed to make 324 ft3 of concrete?
Solution :
Quantity of cement, sand and gravel is 5x, 9x and 13x respectively.
5x + 9x + 13x = 324
27x = 324
x = 324/27
x = 12
Quantity of cement = 5x = 5(12) = 60
Required quantity of cement is 60 ft3.
Problem 5 :
If Andy drove 84 miles in 1 hour 45 minutes, how many miles can he drive in 5 hours?
Solution :
1 hour 45 minutes :
45 minutes = 45/60 hours = 3/4 hours
1 hour 45 minutes = 1¾ hours
Let x be the number of miles.
84 : 1¾ = x : 5
84 : 7/4 = x : 5
84 ⋅ 5 = 7/4 ⋅ x
x = 420 (4/7)
x = 1680/7
x = 240
Number of miles he can drive is 5 hours is 240 miles.
Problem 6 :
A collection of quarters, dimes and nickels is worth $5. If the ratio quarters to dimes to nickels is 2 : 4 : 7, how many quarters are there?
Solution :
$5 = 500 cents
1 quarter = 0.25 cents
1 dime = 0.1 cents
1 nickel = 0.05 cents
Let number of quarters, dimes and nickels be 2x, 4x and 7x.
2x(0.25) + 4x(0.1) + 7x(0.05) = 5
0.5x + 0.4x + 0.35x = 5
1.25x = 5
x = 5/1.25
x = 4
Number of quarters = 2(4) = 8 quarters.
Problem 7 :
If 5x/3 = (x + 14)/2, what is the value of x?
Solution :
5x/3 = (x + 14)/2
By doing cross multiplication, we get
10x = 3(x + 14)
10x = 3x + 42
7x = 42
x = 42/7
x = 6
Problem 8 :
A trail mix contains raisin, peanut, and chocolate. The ratio of raisin to peanut is 2:3 and the ratio of peanut to chocolate is 5:8. What is the ratio of raisin to chocolate?
Solution :
Ratio of raisin to peanut is 2 : 3.
Ratio of peanut to chocolate is 5 : 8.
By finding compound ratio, we get
2 : 3 = 10 : 15
5 : 8 = 15 : 24
10 : 15 : 24
Ratio between raisin and chocolate = 10 : 24.
= 5 : 12
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