Expert: Paul Klarreich - 3/20/2008

Question
2.) Find the values of x and y that solve the following system of equations:We call the two numbers x & y.
7x + 9y = 9
6x + 5y = -14

x =
y =

4.) Find the values of x and y that solve the following system of equations:We call the two numbers x and y.
7x - 6y = 5
-2x + 5y = -8

x =
y =

5.) Find two numbers whose sum is 44 and such that one is 3 times as large as the other. We call the two numbers x and y.

x =
y =

6.) In a family there are two cars. The sum of the average miles per gallon obtained by the two cars in a particular week is 50. The first car has consumed 40 gallons during that week, and the second has consumed 30 gallons, for a total of 1800 miles driven by the two cars combined. What was the average gas mileage obtained by each of the two cars in that week?

First Car: ___miles/gallon
Second Car: ___miles/gallon

7.) A motorboat travels 162km in 3 hours going upstream and 882km in 9 hours going downstream. What is the speed of the boat in still water, and what is the speed of the current?

Boat Speed: ___km/h
Current Speed: km/h

8.) Find two numbers whose sum is 46 and whose difference is 8. We call the two numbers x and y.

x =
y =

9.) Two rainstorms occurred in one week in a certain area. In the first rainstorm 25 ml of rain fell per hour, and in the second rainstorm 20 ml of rain fell per hour. Rain fell that week for a total of 65 hours for a total rainfall of 1500 ml. How long was each of the two rainstorms?

First Storm ___/hr
Second Storm ___/hr

10.) A motorboat travels 549 km in 9 hours going upstream and 776 km in 8 hours going downstream. What is the speed of the boat in still water, and what is the speed of the current?

Boat Speed: ___km/h
Current Speed: ___km/h

I'm having problems solving the above solutions. Can you please help me. Thank you!  

Answer
Questioner:   Sherry
Category:  Advanced Math
Private:  No
 
Subject:  College Algebra

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Hi, Sherry,

Since you didn't tell me what you already tried to do and where you got stuck ("I'm having trouble" does not qualify.), I will confine myself to telling you how to get started.  Besides, this is a lot of problems and I'm sure you don't want me just to do your homework for you.
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Question:  2.) Find the values of x and y that solve the following system of equations:We call the two numbers x & y.
7x + 9y = 9       (A)
6x + 5y = -14     (B)

Try multiplying A by -5 and B by 9, then add to eliminate y.

..................................

4.) Find the values of x and y that solve the following system of equations:We call the two numbers x and y.
A. 7x - 6y = 5
B. -2x + 5y = -8

Try  5A + 6B, same as #2.
.........................

5.) Find two numbers whose sum is 44 and such that one is 3 times as large as the other. We call the two numbers x and y.

Write:
Let x = the larger number,
y = the smaller.

Then their sum:  x + y = 44, and  x = 3y.  Now use substitution to solve.
..........................
6.) In a family there are two cars. The sum of the average miles per gallon obtained by the two cars in a particular week is 50. The first car has consumed 40 gallons during that week, and the second has consumed 30 gallons, for a total of 1800 miles driven by the two cars combined. What was the average gas mileage obtained by each of the two cars in that week?

LET  x = the mpg of the first car
then  40x is the miles driven by the first.

LET  y = the mpg of the second.
then 30y  is the miles driven by the second.

Then  x + y = 50 and
   40x + 30y = 1800.

.................................
7.) A motorboat travels 162km in 3 hours going upstream and 882km in 9 hours going downstream. What is the speed of the boat in still water, and what is the speed of the current?

If  b = the speed of the boat in still water
and c = the speed of the current

then  b + c is the speed downstream and
     b - c is the speed upstream.
................................
8.) Find two numbers whose sum is 46 and whose difference is 8.

We call the two numbers x and y. << That's bad.  Instead: write:

we call the larger number  x  and
the smaller one  y.

[Don't leave out details.  That's lazy and it's how you get stuck.]

................................
9.) Two rainstorms occurred in one week in a certain area. In the first rainstorm 25 ml of rain fell per hour, and in the second rainstorm 20 ml of rain fell per hour. Rain fell that week for a total of 65 hours for a total rainfall of 1500 ml. How long was each of the two rainstorms?

LET x = the NUMBER OF HOURS IN THE FIRST RAINSTORM.

I think you can figure what to do now.
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10.) A motorboat travels 549 km in 9 hours going upstream and 776 km in 8 hours going downstream. What is the speed of the boat in still water, and what is the speed of the current?

See #7.