Mar
01
Need Help Solving These.?
By1. 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?
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.
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%?
1 Comments
March 1st, 2010 at 12:54 pm
1. 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.
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. $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