Need help on a few algabra problems.
solve the equation for the indicated variable
1. F=9/5C+32, for C
2. Kevin invested part of his $10,000 bonus in a certificate of a deposit that paid 6% annual simple intrest, and the remmainder in a mutual fun that paid 11% annual simple interest. if his total interst for that year was $900, how much did Kevin invest in the mutual fund?
3. Ken and Kara are 29 miles apart on a calm lake paddling towards each other. Ken paddles at 4 miles per hour while Kara paddles at 7 miles per hour. How long will it take them to meet?
4. A chemist needs 110 mL of a 65% solution but only has 53% and 97% solutions available. Find how many mL of each that should be mixed to get the desired solution.
Ken is moving at 4 mi/h and covers a distance of x mi in t hours.
Kara is moving at 7 mi/h and covers a distance of y mi in t hours. (Obviously they meet at the same time!)
And we know that, combined, they covered x + y = 29 mi.
Thus:
So
and
So
And
So it takes them about 2.64 hrs to meet.
-Dan
We want a total volume of 110 mL of solution at the end. This means we need
mg of solute.
So we are going to mix "x" mL of the 53% solution with "y" mL of the 97% solution to get x + y = 110 mL of final solution.
We will have mg of solute in the final solution.
So:
From the first equation:
Inserting this into the second equation gives:
Thus we need 80 mL of the 53% solution and 110 mL - 80 mL = 30 mL of the 97% solution.
-Dan