A pension fund owns 2,400 fewer shares in mutual stock funds than mutual bond funds. Currently, the stock funds sell for $14 per share, and the bond funds sell for $17 per share. How many shares of each does the pension fund own if the value of the securities is $146,200?

Question

anonymous · Answer

Need to find amount of:

stock funds shares
bond fundsshares

paxpolaris · Answer

:) ... So let's choose some variables and write some equations.

anonymous · Answer

ok

paxpolaris · Answer

can we use two variables?

S is for stocks, B is for bonds.

anonymous · Answer

ok

paxpolaris · Answer

A pension fund owns 2,400 fewer Stocks than Bonds.

... can you translate this into an equation using S and B

anonymous · Answer

B-2400

paxpolaris · Answer

right the number of Stocks is equal to B-2400

$$\large S= B-2400$$

paxpolaris · Answer

now for the second equation: 
Stocks have a value of  $14 each,  Bonds  have value $17 each.... And the total value is $146,200.

anonymous · Answer

Ok so am I basically dividing 14 and 17 into it

paxpolaris · Answer

?
we need to write another equation using S and B.

anonymous · Answer

ok

paxpolaris · Answer

1 Stock have a value of  $14$
so, S stocks will have value of $14S$

anonymous · Answer

ok

paxpolaris · Answer

same way, 1 Bond has a value of  $17$
so, B stocks will have value of $B\times17=17B$

anonymous · Answer

ok

paxpolaris · Answer

add both $14S$ and $17B$ up .... and we should get the total value of $146200$

paxpolaris · Answer

so the 2nd equation is :$$14S+17B=146200$$

anonymous · Answer

ok that makes sense

paxpolaris · Answer

so we have:
$$S=B-2400$$

and, $$14S+17B=146200$$


can you solve for S and B from here?

anonymous · Answer

not quite

paxpolaris · Answer

well since we know that $S$ is the same number as $B-2400$ from the first equation. 

in the 2nd equation where we see $S$ we can replace it with $(B-2400)$

paxpolaris · Answer

$14S+17B=146200$ will becomes:


$$\large \implies14(B-2400)+17B=146200$$

anonymous · Answer

oh ok

anonymous · Answer

how about the other one?

paxpolaris · Answer

so what do you have for the number of mutual bond fund shares

anonymous · Answer

5800

paxpolaris · Answer

$$\huge \color{green}\checkmark$$

so to find the number of stocks you just have to go back to the first sentence.

anonymous · Answer

5800-2400

anonymous · Answer

3400

paxpolaris · Answer

A pension fund owns 2,400 fewer Stocks than Bonds.
$$S=B-2400\=5800-2400\=3400$$

great job :)

anonymous · Answer

thanks

anonymous · Answer

you were very helpful!

paxpolaris · Answer

yw