Word Problems

[phoenix9801]

1-
The length of the edge of a cube is increased by 3 to yield a cube of volume 343. What was the original length of the edge of the cube?
a) 4
b) 5
c) 6
d) 7
e) 8

2-
Angel, Tim, and Evangeline decide to buy a $400 television. If Angel pays $20 more than Evangeline, and Tim pays twice as much as Angel, how much does Evangeline spend on the television?
a) $ 45
b) $ 65
c) $ 75
d) $ 85
e) $ 105

3-
Alan, Jennie, and Samuel decide to buy a fish tank together. Alan agrees to pay three times as much as Jennie, while Samuel pays $90 less than Alan. If they had decided to each pay the same amount, Samuel would have spent $20 less than he does. How much does Jennie pay for the fish tank?
a) 120
b) 138
c) 150
d) 270
e) 360

4-
Rafa, Roger, and Andy agree to buy a tennis court. Roger agrees to pay 25% more than Andy, and Rafa agrees to pay twice as much as Roger and Andy combined. If the tennis court costs a total of $29,700, how much does Roger pay?
a)$ 4,400
b) $ 5,500
c) $ 9,900
d) $ 10,000
e) $ 19,800

[neelgandham]

The length of the edge of a cube is increased by 3 to yield a cube of volume 343. What was the original length of the edge of the cube?

volume of a cube after the side is increased = side^3 = 343. i.e side = 7
Length of the new side = 7.
Length of the new side = 3 + Length of the old side
7 = 3 + Length of the old side
Length of the old side = 4

[neelgandham]

Angel, Tim, and Evangeline decide to buy a $400 television. If Angel pays $20 more than Evangeline, and Tim pays twice as much as Angel, how much does Evangeline spend on the television?

Let the amount Angel pays be A
Let the amount Tim pays be T
Let the amount Evangeline pays be E. Then

A = 20 + E
T = 2A = 2*(20+E)
A + T + E = 400.
So,
20 + E + 40 + 2E + E = 400
60 + 4E = 400
4E = 340
E = 85

IMO D

[neelgandham]

Alan, Jennie, and Samuel decide to buy a fish tank together. Alan agrees to pay three times as much as Jennie, while Samuel pays $90 less than Alan. If they had decided to each pay the same amount, Samuel would have spent $20 less than he does. How much does Jennie pay for the fish tank?

Let the amount Alan pays be A
Let the amount Jennie pays be J
Let the amount Samuel pays be S. Then

A = 3J
S = A - 90 = 3J - 90.
Total amount to be paid = J + 3J + 3J -90 = 7J - 90. If each paid the same amount then each had to pay (7J-90)/3. In this case Samuel would have spent $20 less, i.e 3J - 90 - 20.
So,
(7J-90)/3 = 3J - 110
7J - 90 = 9J - 330
2J = 240
J = 120

[neelgandham]

Rafa, Roger, and Andy agree to buy a tennis court. Roger agrees to pay 25% more than Andy, and Rafa agrees to pay twice as much as Roger and Andy combined. If the tennis court costs a total of $29,700, how much does Roger pay?

Let the amount Rafa pays be Ra
Let the amount Roger pays be Ro
Let the amount Andy pays be A. Then

Ro = 1.25*A
Ra = 2*(Ro + A) = 2*(1.25A + A) = 4.5A
Total amount paid = Ro + Ra + A = 1.25A + 4.5A + A = 29,700.
6.75A = 29700
A = $4400
Amount Roger pays = Ro = 1.25*A = 1.25*4400 = $5500 IMO B