Question

Erin has three more dimes than nickles and twice as many quarters as dimes. she has a total of $5.05 How many of each type of coin does Erin have

5.05= 2q-d-3d-n

A Piece of rope that is 63 meters long is cut into three pieces such that the second piece is twice as long as the first and the third piece is three meters longer than the second. Find the length of each piece.

2x+3x+x=63

Dukes chain saw requires a ration of oil to gas 1 to 40. How many ounces of oil should he add to one half gallon of gas?

Tom can row at the rate of 12 kilometers per hour in still water. He rows upstream for two hours and returns in one hour and twelve minutes. Find the rate of the current.

D=r*t
R=12 km per hour
T= two hours


I would like help with setting up the equtions for these. I do not need you to solve them I just really need help with setting them up I attempted them but they are not right. I really struggle in this.

Answer 1

Erin has three more dimes than nickles and twice as many quarters as dimes. she has a total of $5.05 How many of each type of coin does Erin have

5.05= 2q-d-3d-n
--------------------
but they have different values
nickels = n, value = .05 n
dimes = (n+3), value = .10(n+3)
quarters = 2(n+3), value = .25(2)(n+3)
so
.05 n + .1 n + .3 + .5 n + 1.5 = 5.05

.65 n + 1.8 = 5.05
.65 n = 3.25
n = 5 nickels
etc

Answer 2

A Piece of rope that is 63 meters long is cut into three pieces such that the second piece is twice as long as the first and the third piece is three meters longer than the second. Find the length of each piece.

2x+3x+x=63
---------------------------
need to be more orderly
first one = f
second one = 2 f
third one = 2 f + 3
so
f+2 f + 2 f + 3 = 63
5 f = 60
f = 12 etc

Answer 3

Dukes chain saw requires a ration of oil to gas 1 to 40. How many ounces of oil should he add to one half gallon of gas?
8 oz = 1 cup
2 cups = 16 oz = 1 pint
2 pints = 32 oz = 1 quart
4 quarts = 128 oz = 1 gallon
By the way " a pint is a pound the world around" :)
so 1/2 gallon is 64 oz
x/64 = 1/40
x = 64/40 = 1.6 oz
(That is about right, like I put in my chain saw)

Answer 4

Tom can row at the rate of 12 kilometers per hour in still water. He rows upstream for two hours and returns in one hour and twelve minutes. Find the rate of the current.

D=r*t
R=12 km per hour
T= two hours
---------------------------
speed upstream = 12 - c
speed downstream = 12 - c
d = 2(12-c)
d = 1 12/60 (12+c)

1 12/60 = 1.2
so
24 - 2 c = 14.4 + 1.2 c

3.2 c = 9.6
c = 3

Answer 5

speed downstream = 12 + c