1. Story Problems

Jim and Joe started on trips from San Francisco and traveled in opposite directions. Jim traveled 15 km/h faster than Joe. After 4 hours, they were 420 km apart. How fast was each person traveling?

A coin bank contains more than $3 in quarters, dimes, and nickels. The # of dimes is twice the # of quarters and the # of nickels is 3 times the # of quarters. Find the least possible # of quarters in the bank. Cynthia invested 3 times as much money at 6% as at %5. If the total of simple interest is at least$1150, what is the least possible amount Cynthia has invested at 5%?

Michael drove to a friend's house at a rate of 40 m/h. He came back by the same route, but at a rate of 45 m/h. If the roundtrip took less than 4 hrs, what is the greatest possible distance Michael could have traveled to visit his friend?

Caridad is6 years older than her sister. For years ago she was 4 times as old as her sister. How old is Caridad now?

Jims average score on 3 tests is 82. What is the least he can score on his 4th test so his average will be at least 86?

2. Originally Posted by peachgal

Jim and Joe started on trips from San Francisco and traveled in opposite directions. Jim traveled 15 km/h faster than Joe. After 4 hours, they were 420 km apart. How fast was each person traveling?

Let Joe's speed = x km/h
so, Jim's speed = (x+15) km/h

Distance travelled by Joe in 4 hours= speed . time = 4x

Distance travelled by Jim in 4 hours= 4(x + 15)

Total distance = 420

4x + 4(x + 15) = 420

Now solve it.

3. Originally Posted by peachgal

A coin bank contains more than $3 in quarters, dimes, and nickels. The # of dimes is twice the # of quarters and the # of nickels is 3 times the # of quarters. Find the least possible # of quarters in the bank. Let # dimes = d # nickels = n # quarters = q d = 2q and n = 3q Total money, 0.25q + 0.10d + 0.05n > 3 0.25q + 0.10 (2q) + 0.05 (3q) > 3 Now solve. 4. Originally Posted by peachgal Please and Thank you Cynthia invested 3 times as much money at 6% as at %5. If the total of simple interest is at least$1150, what is the least possible amount Cynthia has invested at 5%?
Let money invested at 5% = $x So, money invested at 6% =$ 3x

simple interest =

$\displaystyle 0.05x + 0.06 (3x) \ge 1150$

now solve.

5. Originally Posted by peachgal

Michael drove to a friend's house at a rate of 40 m/h. He came back by the same route, but at a rate of 45 m/h. If the roundtrip took less than 4 hrs, what is the greatest possible distance Michael could have traveled to visit his friend?
Let distance to his friend's house = x metres.

Time taken to go $\displaystyle = \frac{\text{Distance}}{\text{speed}}=\frac{x}{40}$

Time taken to come back $\displaystyle = \frac{\text{Distance}}{\text{speed}}=\frac{x}{45}$

Total time < 4 h

$\displaystyle \frac{x}{40} + \frac{x}{45} <4$

Now, finish up.

6. Originally Posted by peachgal
Caridad is 6 years older than her sister. For years ago she was 4 times as old as her sister. How old is Caridad now?
Her sister's age = x yrs.

Caridad's age = (x + 6) yrs.

Four years ago,

Her siter's age = x - 4

Caridad's age = x + 6 - 4 = x + 2

Now,

x + 2 = 4 (x - 4)

Now, finish up. did you get it???

7. Originally Posted by peachgal
Total score of first 3 tests $\displaystyle = 3 \times 82 = 246$
Total score of all 4 tests $\displaystyle = 4 \times 86 = 344$