SOLUTION: 1. Joe has a collection of nickels and dimes that is worth $5.65. If the number of dimes were doubled and the number of nickels were increased by 8, the value of the coins would be

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: 1. Joe has a collection of nickels and dimes that is worth $5.65. If the number of dimes were doubled and the number of nickels were increased by 8, the value of the coins would be      Log On

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Question 170949: 1. Joe has a collection of nickels and dimes that is worth $5.65. If the number of dimes were doubled and the number of nickels were increased by 8, the value of the coins would be $10.45. How many dimes does he have?
2. An express and local train leave Gray’s Lake at 3 P.M. and head for Chicago 50 miles away. The express travels twice as fast as the local, and arrives 1 hour ahead of it. Find the speed of each train.
3. Walt made an extra $9000 last year from a part-time job. He invested part of the money at 9% and the rest at 8%. He made a total of $770 in interest. How much was invested at 8%?
Answer by Mathtut(3670) About Me  (Show Source):
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1. lets call the number of nickels and dimes, n and d , respectively.
:
.05n+.1d=5.65............eq 1
.05(n+8)+.1(2d)=10.45....eq 2
:
lets distribute and collect terms from eq 2
:
.05n+.4+.2d=10.45
.05n+.2d=10.05....revised eq 2
:
now lets subtract eq 1 from revised eq 2 and eliminate the n terms .05n-.05n=0
we end up with .2d-.1d and 10.05-5.65
:
.2d-.1d=10.05-5.65
:
.1d=4.4
:
highlight%28d=44%29dimes
:
now plug in d's found value into either equation. I choose eq 1
:
.05n+.1(44)=5.65---->.05n=1.25
:
highlight%28n=25%29nickels
:
2) d=rt. we know the distance in both cases is 50. Lets call the local trains rate r and its time t. So the express's rate would be 2r and its time t-1
:
50=rt..........eq 1
50=2r(t-1).....eq 2
:
lets rewrite eq 1 as t=50/r and plug that value into eq 2
:
50=2r%28%2850%2Fr%29-1%29----->50=2r%28%2850-r%29%2Fr%29----
50=2cross%28r%29%2850-r%29%2Fcross%28r%29
50=100-2r---->-2r=-50
highlight%28r=25%29MPH-speed of the local train
highlight%282%2825%29=50%29MPH-speed of the express
:
3)amount invested times rate of interest will equal interest earned. In this case we have two different amounts. amount at 9% we will call x so the amount invested at 8% will be 9000-x. Multiply each of those by there respective interest rates and that will equal 770
:
.09x+.08(9000-x)=770
:
.09x+720-.08x=770
:
.01x=50
:
highlight%28x=5000%29dollars invested at 9%
highlight%289000-5000=4000%29dollars invested at 8%