Difference between revisions of "2006 AMC 10B Problems"
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== Problem 22 == | == Problem 22 == | ||
+ | Elmo makes <math>N</math> sandwiches for a fundraiser. For each sandwich he uses <math>B</math> globs of peanut butter at <math>4</math>¢ per glob and <math>J</math> blobs of jam at <math>5</math>¢ per blob. The cost of the peanut butter and jam to make all the sandwiches is <math>\$2.53</math>. Assume that <math>B</math>, <math>J</math>, and <math>N</math> are positive integers with <math>N>1</math>. What is the cost of the jam Elmo uses to make the sandwiches? | ||
+ | |||
+ | <math> \mathrm{(A) \ } \$1.05\qquad \mathrm{(B) \ } \$1.25\qquad \mathrm{(C) \ } \$1.45\qquad \mathrm{(D) \ } \$1.65\qquad \mathrm{(E) \ } \$1.85 </math> | ||
[[2006 AMC 12B Problems/Problem 22|Solution]] | [[2006 AMC 12B Problems/Problem 22|Solution]] |
Revision as of 16:24, 13 July 2006
Contents
- 1 Problem 1
- 2 Problem 2
- 3 Problem 3
- 4 Problem 4
- 5 Problem 5
- 6 Problem 6
- 7 Problem 7
- 8 Problem 8
- 9 Problem 9
- 10 Problem 10
- 11 Problem 11
- 12 Problem 12
- 13 Problem 13
- 14 Problem 14
- 15 Problem 15
- 16 Problem 16
- 17 Problem 17
- 18 Problem 18
- 19 Problem 19
- 20 Problem 20
- 21 Problem 21
- 22 Problem 22
- 23 Problem 23
- 24 Problem 24
- 25 Problem 25
- 26 See also
Problem 1
What is ?
Problem 2
For real numbers and
, define
. What is
?
Problem 3
A football game was played between two teams, the Cougars and the Panthers. The two teams scored a total of 34 points, and the Cougars won by a margin of 14 points. How many points did the Panthers score?
Problem 4
Circles of diameter 1 inch and 3 inches have the same center. The smaller circle is painted red, and the portion outside the smaller circle and inside the larger circle is painted blue. What is the ratio of the blue-painted area to the red-painted area?
Problem 5
A rectangle and a
rectangle are contained within a square without overlapping at any point, and the sides of the square are parallel to the sides of the two given rectangles. What is the smallest possible area of the square?
Problem 6
A region is bounded by semicircular arcs constructed on the side of a square whose sides measure , as shown. What is the perimeter of this region?
Problem 7
Which of the folowing is equivalent to when
Problem 8
A square of area 40 is inscribed in a semicircle as shown. What is the area of the semicircle?
Problem 9
Francesca uses 100 grams of lemon juce, 100 grams of sugar, and 400 grams of water to make lemonade. There are 25 calories in 100 grams of lemon juice and 386 calories in 100 grams of sugar. Water contains no calories. How many calories are in 200 grams of her lemonade?
Problem 10
In a triangle with integer side lengths, one side is three times as long as a second side, and the length of the third side is 15. What is the greatest possible perimeter of the triangle?
Problem 11
What is the tens digit in the sum
Problem 12
The lines and
intersect at the point
. What is
?
Problem 13
Joe and JoAnn each bought 12 ounces of coffee in a 16 ounce cup. Joe drank 2 ounces of his coffee and then added 2 ounces of cream. JoAnn added 2 ounces of cream, stirred the coffee well, and then drank 2 ounces. What is the resulting ratio of the ammount of cream in Joe's coffee to that in JoAnn's coffee?
Problem 14
Let and
be the roots of the equation
. Suppose that
and
are the roots of the equation
. What is
?
Problem 15
Rhombus is similar to rhombus
. The area of rhombus
is
and
. What is the area of rhombus
?
Problem 16
Leap Day, February 29, 2004, occured on a Sunday. On what day of the week will Leap Day, February 29, 2020, occur?
Problem 17
Bob and Alice each have a bag that contains one ball of each of the colors blue, green, orange, red, and violet. Alice randomly selects one ball from her bag and puts it into Bob's bag. Bob then randomly selects one ball from his bag and puts it into Alice's bag. What is the probability that after this process the contents of the two bags are the same?
Problem 18
Let be a sequence for which
,
, and
for each positive integer
.
What is ?
Problem 19
A circle of radius is centered at
. Square
has side length
. Sides
and
are extended past
to meet the circle at
and
, respectively. What is the area of the shaded region in the figure, which is bounded by
,
, and the minor arc connecting
and
?
Problem 20
In rectangle , we have
,
,
, for some integer
. What is the area of rectangle
?
Problem 21
For a particular peculiar pair of dice, the probabilities of rolling ,
,
,
,
, and
, on each die are in the ratio
. What is the probability of rolling a total of
on the two dice?
Problem 22
Elmo makes sandwiches for a fundraiser. For each sandwich he uses
globs of peanut butter at
¢ per glob and
blobs of jam at
¢ per blob. The cost of the peanut butter and jam to make all the sandwiches is
. Assume that
,
, and
are positive integers with
. What is the cost of the jam Elmo uses to make the sandwiches?