# Thread: few algabra questions, need help!

1. ## few algabra questions, need help!

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.

2. Originally Posted by mathnoobie25
solve the equation for the indicated variable
1. F=9/5C+32, for C
$\displaystyle F = \frac{9}{5}C + 32$

$\displaystyle F - 32 = \frac{9}{5}C + 32 - 32$

$\displaystyle F - 32 = \frac{9}{5}C$

$\displaystyle \frac{5}{9}(F - 32) = \frac{5}{9} \cdot \frac{9}{5}C$

$\displaystyle \frac{5}{9}(F - 32) = C$

-Dan

3. Originally Posted by mathnoobie25
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?
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:
$\displaystyle 4 = \frac{x}{t}$

So
$\displaystyle x = 4t$

and
$\displaystyle 7 = \frac{y}{t}$

So
$\displaystyle y = 7t$

And
$\displaystyle x + y = 29$

$\displaystyle 4t + 7t = 29$

$\displaystyle 11t = 29$

$\displaystyle \frac{1}{11} \cdot 11t = \frac{1}{11} \cdot 29$

$\displaystyle t = \frac{29}{11}$

So it takes them about 2.64 hrs to meet.

-Dan

4. Originally Posted by mathnoobie25
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.
We want a total volume of 110 mL of solution at the end. This means we need
$\displaystyle 0.65 \cdot 110 = 71.5$ 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 $\displaystyle 0.53 \cdot x + 0.97 \cdot y = 71.5$ mg of solute in the final solution.

So:
$\displaystyle x + y = 110$
$\displaystyle 0.53x + 0.97y = 71.5$

From the first equation:
$\displaystyle y = 110 - x$

Inserting this into the second equation gives:
$\displaystyle 0.53x + 0.97(110 - x) = 71.5$

$\displaystyle 0.53x + 106.7 - 0.97x = 71.5$

$\displaystyle -0.44x = -35.2$

$\displaystyle x = 80$

Thus we need 80 mL of the 53% solution and 110 mL - 80 mL = 30 mL of the 97% solution.

-Dan