College Algebra Math word problem?
Bobs coin bank contains nickels, dimes, and quarters. There are twice as many dimes as quarters, and and seven more nickels than dimes. The total value of the coins is $3.10. How many of each coin are there?
A passenger train travels 295 miles in the same amount of time it takes a freight train t travel 225 miles. the rate of the passenger train is 14mph greater than the rate of the freight train. Find the rate of each train.
Comments
let n= #nickels so 0.05n= value of the nickels
let d= # dimes so 0.10d= value of the dimes
let q =# quarters so 0.25q = value of the quarters
We are told that d=2q
and n = d + 7 so n = 2q +7 We will use these facts to replace n and d
we know 0.05n + 0.10d + 0.25q = 3.10
so 0.05(2q +7) + 0.10(2q) + 0.25q = 3.10
0.10q + 0.35 + 0.20q +0.25g = 3.10
0.55q = 2.75
q=5 quarters
d= 2(5)= 10 dimes
n= 2(5) + 7 = 17 nickels
295 = (r + 14)t and 225 = rt
295= rt + 14t
295 = rt + 14t
-225=-rt
-------------------
70 = 14t
t= 5 hrs
225 = r*5
r= 45mph for the freight train
45 +14 = 59 mph for the passenger train
Let x = number quarters
So 2x = number of dimes //// There are twice as many dimes as quarters
& (2x+7) = number of nickels ///// There are seven more nickels than dimes
5(2x+7) + 10(2x) + 25x = 310
10x +35 +20x +25x = 310
55x = 310 -35
55x = 275
x = 275/55 = 5
There are 5 quarters , 10 dimes & 27 nickels.
Let v = speed of freight train
Use d = vt
so 225 = vt (1)
Speed of passenger train is (v+14) mph
so 295 = (v+14)t (2)
295 = vt + 14t
295 = 225 + 14t /// from (1) vt =225
70 = 14t
t = 70/14 = 5 hours
Train speeds;
Freight train = d/t = 225/5 = 45 mph
Passengar = 45 + 14 = 59 mph
Or do it this way
295/5 = 59 mph
1) let n = nickels, d = dimes, and q = quarters
d = 2q --> 1/2d = q
n = 7 + d
3.10 = .1d + .05n + .25q
--> 3.10 = .1d + .05(7+d) + .25(d/2)
--> 310 = 10d + 35 + 5d + 25/2d
--> 275 = 27.5d
--> d = 10
--> n = 17
--> q = 5
17 nickels, 10 dimes, 5 quarters
2) d = rt
--> 295/(rp) = 225/(rf)
--> rp = rf + 14
--> 295(rf) = 225(rf + 14)
--> 70(rf) = 3150
--> rf = 45
--> rp = 59
Passenger Train = 59mph, Freight Train = 45mph
let x = no. of quaters
2x=dimes
2x+7=nickels
x(25)+x2(10)+(2x+7)(5)=3.10
25x+20x+10x+35=3.10
55x=275
x=5...
295/x+14=225/x
70x=3150
x=45
that's probably right tho