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.
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
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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
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
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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
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)
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
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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
speed downstream = 12 + c
Sure, I can help you set up the equations for these problems. Let's go through each problem step by step:
1. Erin's Coins:
Let's assume Erin has x nickels. According to the problem, Erin has three more dimes than nickels, so she has x + 3 dimes. Also, she has twice as many quarters as dimes, so she has 2(x + 3) = 2x + 6 quarters. The total value of all the coins is $5.05. So we can set up the equation:
0.05(x) + 0.1(x + 3) + 0.25(2x + 6) = 5.05
2. Rope Length:
Let's assume the length of the first piece is x meters. According to the problem, the second piece is twice as long as the first, so its length is 2x meters. The third piece is three meters longer than the second, so its length is 2x + 3 meters. The total length of the rope is 63 meters. So we can set up the equation:
x + 2x + (2x + 3) = 63
3. Oil and Gas:
Let's assume the amount of oil Duke should add is x ounces. According to the problem, the ratio of oil to gas is 1 to 40. One-half gallon of gas is equal to 64 ounces. So we can set up the equation:
x/64 = 1/40
4. Tom's Rowing:
Let's assume the rate of the current is x kilometers per hour. According to the problem, Tom's rowing speed in still water is 12 kilometers per hour. He rows upstream for two hours, so the effective speed is 12 - x kilometers per hour. He returns in one hour and twelve minutes, which is 1.2 hours, so the effective speed is 12 + x kilometers per hour. So we can set up the equation:
(12 - x) * 2 = (12 + x) * 1.2
These are the equations you can set up for each problem. Now you can solve them individually. If you need any further assistance in solving them, feel free to ask.