Name:
Block:
Date:
February
, 2008
Geometry: 7.1: Some Ratio and Percentage Problems
Teacher: Mrs. Chou
Background/Introduction/Instructions: Unit 7 will discuss quadrilaterals, figures with ______ sides, in depth.
To get started with this unit, some at-home preparation is necessary. Today, we will take a day to review some
concepts regarding ratio and percents. The topics discussed in this worksheet will appear on your first unit 7
quiz, and on your unit 7 test.
1.
Percent means per ____________.
2. If A is
7
of B, that means that A = _______B. (Insert a fraction into the blank).
11
3. If A is 120% of B, that means that A = ________B. (Insert a decimal number into the blank.)
!
4. If A is 120% of B, that means that A = ________B. (Insert a fraction in lowest terms into the blank.)
5. If the ratio of A:B is 4:7, then
A ?
= .
B ??
6. If the ratio of A:B is 4:7, then A = _________B. (Insert a fraction in lowest terms into the blank).
!
State whether each of the following is true (T) or False (F).
3
4
of B means B is
of A.
4
3
3
4
8. A is % of B means B is
of A.
4
3
7.
A is
9. If A is 5% more than B, then B is 5% less than A.
!
!
!
10. If A increases by 8% and then decreases by 8%, the result is equal to A.
!
11. If A increases by 10% and then further increases by 5%, the overall increase is equal to 15% of A.
12. A is given a 5% increase followed by a 10% decreases. This is the same as when A is given a single 5%
decrease.
13. A is given a 5% increase followed by a 10% decrease. This is the same as when A is given a 10% decrease
followed by a 5% increase.
14. If A increases by 10%, its value becomes B. Then A is 90% of B.
15. If A increases by 10%, its value becomes B. Then B is 110% of A.
16. If A is 35% of B, then A:B is 35:100.
17. If A is 35% of B, then B:A is 65:35.
18. A:B is 3:4 means that A is
3
of B.
7
19. A:B is 3:4 means that A is 75% of B.
20. A:B is 3:4 means!
that B is 75% of A.
21. In a class, the ratio of the number of boys to the number of girls is 3:4. This means that the number of
boys is
3
the number of kids in the class.
4
22. A increases in the ratio 5:4 means A increases by
5
%.
4
23. A increases in the ratio 5:4 means A increases by 125%.
!
24. A increases in the ratio 5:4 means A increases by 25%.
!
25. If A:B =
1 1
: , then A:B = y:x.
x y
26. The number of boys in a class is a% and the number of girls is (a + 10)%. This means the number of girls is
10% more than the number of boys.
!
27. A is 200% of B means A is twice B.
28. A is 200% more than B means A is twice B.
29. The rate of consumption of gasoline by a specific car is 4 gallons per 100 miles. This means that it uses
gasoline at a rate of 0.04gal/mile.
30. The consumption of gasoline by a car is 4 gallons per 100 miles. This means it travels at a rate of
25mi/gallon.
31. In a class, there are 20% more girls than boys. This means 60% of the class are girls and 40% are boys.
The following are fill-in-the-blank.
32. If A increases by 20%, its value becomes B. Therefore A is ______% of B.
33. If A is 45% of B, then B:A is _____ : _____. (Fill in the blanks with two integers to make the statement
true.)
34. A:B is 3:5 means that B is _________% of A.
35. In a class, the ratio of the number of boys to the number of girls is 2:3. This means that the number of
boys is ________ the number of kids in the class. (Insert either a fraction or a percentage that would
make this statement true.)
36. The number of boys in a class is a% and the number of girls is (a + 10)%. The value of a must equal ____.
37. A is 300% of B. Therefore A is ________B. (Insert a number into the blank.)
38. A is 300% more than B. Therefore, A is __________B. (Insert a number into the blank.)
39. A is 350% of B. Therefore A is _______B. (Insert a number into the blank.)
40. A is 350% more than B. Therefore A is ________B. (Insert a number into the blank.)
41. A is 428% of B. Therefore A is _______B. (Insert a number into the blank.)
42. A is 428% more than B. Therefore A is ________B. (Insert a number into the blank.)
The rest of the problems are just problems, not true/false, and not fill-in-the-blank.
43. Walking at an average speed of 5km/h, Alan took 24 minutes to travel from home to his office and arrived
at 7:55am. Calculate how far Alan walked.
44. A man walks a distance of 600m at an average speed of 4km/h and then, without stopping, jogs a further
distance of 1.4km in 7 minutes. Calculate:
(a) the time, in minutes, he takes to walk the 600m,
(b) his jogging speed in km/h,
(c) his average speed for the whole journey in km/h.
45. The speed of a car is 90km/h. Express the speed in m/s.
46. Eliza rides her bike from Sunnyvale to San Mateo, along El Camino in 3hours. Jazmin completes the same
trip in 45minutes less time than Eliza. Jazmin rides at a rate 3mi/hour faster than Eliza. Find the distance
between Sunnyvale and San Mateo.
47. Imagine a suspension bridge 4000ft long. On a hot day the bridge surface expands lengthwise by two feet.
The bridge surface remains rigid, except that it rises at the exact middle so that cars have to go up and
over a hump. Each half is now 2001 feet long. How far above its normal position does the bridge rise?