Question 193333: Please check my work and let me know if I have the right answers, thank you.
Applications of Linear Equations
1. Joe has a collection of nickels and dimes that is worth $6.05. If the number of dimes was doubled and the number of nickels was decreased by 10, the value of the coins would be $9.85. How many dimes does he have?
43 dimes
x * $0.1 + y * $0.05 = $6.05
x * 2 * $0.1 + (y - 10) * $0.05 = $9.85
Solve for x in equation 1
x * $0.1 = $6.05 - y * $0.05
x = $60.5 - $0.5y
Plug into equation 2
($60.5 - $0.5y) * 2 * $0.1 + (y - 10) * $0.05 = $9.85
$12.1 - $0.1y + $0.05y - $0.5 = $9.85
$1.75 = $0.05y
y = 35 nickels
x * $0.1 + 35 * $0.05 = $6.05
$0.1x = $4.30
x = 43 dimes
Confirm result, does
43 * 2 * $0.1 + (35 - 10) * $0.05 = $9.85
$9.85 = $9.85
Yes
2. An express train and a local train both leave Gray’s Lake at 12:00 noon and head for Chicago 60 miles away. The express travels twice as fast as the local and arrives 2 hours ahead of it. Find the speed of each train.
v1 = speed of express train
v2 = speed of local train
v1 = 30 MPH
V2 = 15 MPH
v = d/t (velocity = distance / time)
t = d/v
t1 = 60 miles / 30 MPH
t1 = 2 hours
t2 = 60 miles / 15 MPH
t2 = 4 hours
Does, t1 = t2 - 2
2 hours = 2 hours
Yes
3. Walt made an extra $12,000 last year from a part-time job. He invested part of the money at 7% and the rest at 9%. He made a total of $970 in interest. How much was invested at 7%?
$5500 invested at 7%
x + y = $12,000
x * 0.07 + y * 0.09 = $970
x = $12,000 - y
($12,000 - y) * 0.07 + y * 0.09 = $970
$840 - 0.07y + 0.09y = $970
0.02y = $130
y = $6500 @ 9%, which means x = $5500 @ 7%
Double check, does
$5500 * 0.07 + $6500 * 0.09 = $970
$970 = $970
Yes
Found 2 solutions by RAY100, solver91311:
Answer by RAY100(1637)   (Show Source):
You can put this solution on YOUR website! VERY Good Job!!!!!!!!
All answers are correct and you already know this because you checked them ,,,extra goodness.
In problem 2) you stated the answer without the calculations. Perhaps just a typo.
if not you might include something like
60/v1=60/2v2=(60/v2)-2
60=120-4v2
v2=15, and therefore v1=30
Again,,,,please keep up the good work
Answer by solver91311(24713)  (Show Source):
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