# Thread: System of Equation word problem

1. ## System of Equation word problem

A store sells cashews for $6.00 per pound and peanuts for$3.00 per pound. The manager decides to mix 30 pounds of peanuts with some cashews and sell the mixture for \$4.00 per pound. How many pounds of cashews should be mixed with the peanuts so that the mixture will produce the same revenue as would selling the nuts separately?

The answer, from the back of the book, is 15 pounds of cashews.

This is what I've done so far..
$
6x + 3y = 4
$

$
x + y = 30
$

$
6x + 3y = 4
$

$
-3x -3y = -90
$

$
3x = -86
$

Well you can't have negative amount of pounds, so this is wrong...

2. $6*x+30*3=4*(x+30)$
$6*x+90=4*x+120$
$2*x=30$
x=15

3. Thanks for helping with that one rubic!

Here is another one, I am stumped on it. The book is terrible and does not give an example.

With a tail wind, a small aircraft can fly 840 miles in 3 hours. Against this same wind, the plane can fly the same distance in 4 hours. Find the average wind speed and the average airspeed of the plane.

The answers, from the book are:
Average wind speed: 35 mph
Average plane airspeed: 245 mph

4. Here is another one, I am stumped on it. The book is terrible and does not give an example.

With a tail wind, a small aircraft can fly 840 miles in 3 hours. Against this same wind, the plane can fly the same distance in 4 hours. Find the average wind speed and the average airspeed of the plane.

(wind+speed)*3 = 840
wind+speed = 280
(speed-wind)*4 = 840
(speed-wind) = 210

two equation two unknown
wind+speed = 280
speed-wind = 210

2*speed = 490
speed = 245

245 - wind = 210
wind = 35

5. Another one:

A doctor's prescription calls for a daily intake containing 30mg of vitamin C and 20 mg of vitamin D. Your pharmacy stocks two compounds that can be used: one contains 50% vitamin C and 50% vitamin D, the other 40% vitamin C and 20% vitamin D. How many milligrams of each compound should be mixed to fill the prescription?