• May 8th 2007, 01:02 PM
poeticprincess
Use the 5-step method to solve.

1. Jim has a total of 50 coins. Some are nickels and some are dimes. Altogether he has \$4.15. How many dimes and nickels does he have?

2. A sailboat travels 20 miles downstream in 3 hours. It returns in 4 hours. Find the speed of the sailboat in still water and the rate of the current.

3. When the digits of a two-digit number are reversed the new number is 9 more than the original number, and the sum of the digits of the original number is 11. What is the original number?

4. Erin's age is 3 times Waren's. In 4 years she will be twice as old as he will be. how old is each now?

• May 8th 2007, 05:47 PM
topsquark
Quote:

Originally Posted by poeticprincess
1. Jim has a total of 50 coins. Some are nickels and some are dimes. Altogether he has \$4.15. How many dimes and nickels does he have?

Let the number of nickels be n and the number of dimes be d.

Then
n + d = 50
0.05*n + 0.10*d = 4.15

Solving the top equation for d:
d = 50 - n

Insert this into the bottom equation:
0.05*n + 0.10*[50 - n] = 4.15

0.05*n + 5.00 - 0.10*n = 4.15

-0.05*n = 4.15 - 5.00 = -0.85

n = (-0.85)/(-0.05) = 17

Thus d = 50 - 17 = 33

-Dan
• May 8th 2007, 05:56 PM
topsquark
Quote:

Originally Posted by poeticprincess
2. A sailboat travels 20 miles downstream in 3 hours. It returns in 4 hours. Find the speed of the sailboat in still water and the rate of the current.

Let the +x direction be the direction of the current. Let the distance the sailboat travels downstream be d = 20 miles. Let the speed of the boat in still water be v (with respect to the water.) Let the speed of the water be w (with respect to the ground.)

So the speed of the boat downstream with respect to the ground is v + w. So it covers the distance d in a time t given by:
d = (v + w)t --> t = 3 hours

When the boat moves upstream its speed with respect to the ground will be v - w. So it covers the distance d in a time T given by:
d = (v - w)T --> T = 4 hours

Thus
20 = 3(v + w) = 3v + 3w
20 = 4(v - w) = 4v - 4w

Solve the top equation for w:
w = (1/3)(20 - 3v) = (20/3) - v

Insert this into the bottom equation:
20 = 4v - 4[(20/3) - v]

20 = 4v - (80/3) + 4v

8v = 20 + (80/3) = 140/3

v = 140/24 = 35/6 mph

So w = (20/3) - 35/6 = 5/6 mph

-Dan
• May 8th 2007, 06:01 PM
topsquark
Quote:

Originally Posted by poeticprincess
3. When the digits of a two-digit number are reversed the new number is 9 more than the original number, and the sum of the digits of the original number is 11. What is the original number?

Call the number xy, that is to say 10*x + y. If we reverse the number we get yx, that is to say 10*y + x and we know that yx = xy + 9 or
(10*y + x) = (10*x + y) + 9

And
x + y = 9

Solve this equation for y:
y = 9 - x

Insert this into the first equation:
10*[9 - x] + x = 10*x + [9 - x] + 9

90 - 10x + x = 10x + 9 - x + 9

90 - 9x = 9x + 18

18x = 72

x = 72/18 = 4

Thus y = 9 - 4 = 5

So the number is 45.

-Dan
• May 8th 2007, 06:03 PM
topsquark
Quote:

Originally Posted by poeticprincess
4. Erin's age is 3 times Waren's. In 4 years she will be twice as old as he will be. how old is each now?

Let Erin's age be x and Waren's age be y. Then
x = 3y
x + 4 = 2(y + 4)

So inserting the top equation into the bottom:
3y + 4 = 2(y + 4)

3y + 4 = 2y + 8

y = 4

So x = 3*4 = 12.

-Dan
• May 9th 2007, 02:25 PM
poeticprincess
Thnx a lot topsquark! :)