Word Problem

[phoenix9801]

1-
In a certain game of cards, Morgan earned an average of 15 points in each of the first three hands. In the remaining 5 hands, she earned an average of p points per hand. In terms of p, how many points did Morgan earn for the entire game?

A) 3p + 45
B) 3p + 15
C) 5p
D) 5p + 15
E) 5p + 45

2-
If the area of an isosceles right triangle is equal to the perimeter of a square with an area of 4, what is the ratio of the height of the triangle to the side of the square?

A) 1:1
B) 1:2
C) 2:1
D) 2 square root 2
E) 4 square root 2

3-
30 more than ¼ of all the contestants on a reality-television design show are making dresses and 1/3 of those making dresses are making baby-doll dresses. If 1/6 of all the contestants on the show are making baby-doll dresses, how many contestants are on the show?


A) 480
B) 360
C) 240
D) 200
E) 120

[neelgandham]

In a certain game of cards, Morgan earned an average of 15 points in each of the first three hands. In the remaining 5 hands, she earned an average of p points per hand. In terms of p, how many points did Morgan earn for the entire game?

A) 3p + 45
B) 3p + 15
C) 5p
D) 5p + 15
E) 5p + 45

Points won during the first 3 hands = 3*15 = 45
Points won during the next 5 rounds = 5*p = 5p
Total number of points won = 5p + 45

[neelgandham]

If the area of an isosceles right triangle is equal to the perimeter of a square with an area of 4, what is the ratio of the height of the triangle to the side of the square?

A) 1:1
B) 1:2
C) 2:1
D) 2 square root 2
E) 4 square root 2

Let the length of the perpendicular sides be x(isosceles right triangle).
Then, Area of the isosceles right triangle is equal to (1/2)*x*x square units.
Perimeter of of a square with an area of 4 = 8 units.
(Area = side * side = 4=> Side ^2 = 4 and side = 2. Perimeter of a square = 4*side = 4*2 = 8 units)
Given that
Area of the isosceles right triangle = Perimeter of of a square. i.e.
(1/2)*x*x = 8
x = 4.

So, the ratio of the height of the triangle to the side of the square = 4/2 = 2:1(Check the values in RED)

[neelgandham]

30 more than 1/4 of all the contestants on a reality-television design show are making dresses and 1/3 of those making dresses are making baby-doll dresses. If 1/6 of all the contestants on the show are making baby-doll dresses, how many contestants are on the show?

A) 480
B) 360
C) 240
D) 200
E) 120

Let the total number of contestants be C. Then
The number of contestants who make dresses = 30 + (1/4)*C
The number of contestants who make baby-doll dresses = (1/3)*(30 + (1/4)*C) and also
The number of contestants who make baby-doll dresses = (1/6)*C
So, (1/6)*C = (1/3)*(30 + (1/4)*C)
C = 2*(30 + (1/4)*C)
C = 60 + 0.5*C
0.5C = 60
C = 120