# word problems, eqns in two variables, interest, pipes, ....

#### nikki26

##### New member
I am stuck of the following problems:

1. The interstate speed limit for cars is 75 miles per hour in Nebraska, Nevada, and New Mexico,Oklahoma, South Dakota, Utah, and Wyoming and is the highest in the United States. To discourage passing, minimum speeds are posted, so that the difference between the fastest and the slowest moving traffic is no more than 20 miles per hour. Therefore the speed x of a car must satisfy the inequality 55 <= x >= 75.

2. Linear equation of two variables:

. . .y = (1/2)x
. . .y = (-3/4)x + 5

. . .6x - y = 10
. . .y = (-3/4)x - 1

I know that that have to substitute:

. . .6x - ((-3/4)x - 1) = 10
. . .6x + (3/4)x + 1 = 10
. . . . . . . . . . . . .-1. . .-1
. . .(6 + 3/4)x = 9

But I know that I have done something that is incorrect.

4. Interest: A man invests $2200 in three accounts that pay 6%,8%, and 9% annual interest, respectively. He has three times as much invested at 9% as he does at 6%. If his total interest for the year is$178, how much has he invested?

5. Filling a Pool: A pool can be filled by an inlet pipe in 8 hours. The drain will empty the pool in 12 hours. How long will it take to fill the pool if both the inlet pipe and the drain are open?

#### stapel

##### Super Moderator
Staff member
1) The inequality listed at the end of the exercise doesn't make any sense. Does the book maybe read as "55 < x < 75"? And what are you supposed to do with this exercise? (There is no actual question included.)

2) Are the first two equations a system that you need to solve? Are the last two equations another system that you need to solve? Why do you say that you "know" you've done something wrong?

4) Pick a variable for the amount invested at 6%. Write an expression for the amount invested at 9%. Take 2200 and subtract from it the variable and the expression. Simplify to get an expression for the amount invested at 8%.

Multiply each investment variable or expression by the appropriate investment percentage rate. This gives you the interest expressions for each investment.

Sum the interest expressions, and set equal to the given interest amount. Solve for the variable. Back-solve for the investment amounts.

5) Convert the times to rates:

. . .time (in hours) to complete job:
. . . . .inlet: 8
. . . . .drain: 12
. . . . .together: t

. . .completed per time unit
. . . . .inlet: 1/8
. . . . .drain: ??
. . . . .together: ??

Complete the table. Note that the drain is subtracting from what the inlet accomplishes. Combine their per-hour accomplishments, and set equal to their "together" expression. Solve the rational equation for "t".

If you get stuck, please reply showing how far you have gotten. Thank you.

Eliz.

#### nikki26

##### New member
Interest Word Problem

4) Interest: A man invests $2200 in three accounts that pay 6%,8%, and 9% annual interest, respectively. He has three times as much invested at 9% as he does at 6%. If his total interest for the year is$178, how much has he invested?

I did not understand what you meant about the word problem. Could you go into further detail?

#### stapel

##### Super Moderator
Staff member
Re: Interest Word Problem

nikki26 said:
4) Interest: ...

I did not understand what you meant about the word problem. Could you go into further detail?
Where did you get lost? Please reply showing the steps you could follow (starting with picking a variable), and how far you could get.

Thank you.

Eliz.