story problem help pre algebra.............

Question

Norman and Suzanne own 26 share of a fast food restaurant stock and 76 shares of a toy company stock. At the close of the markets on a particular day in 2004, their stock portfolio consisting of these two stocks was $1569.00. The closing price of the fast food restaurant stock was $27 more per share than the toy company. What was the closing price of each stock?

Answer 1

Here we have two unknowns: the closing price of the fast food restaurant stock, and the closing price of the toy company stock. With two unknowns, we must have two equations in order to solve.

Let F = fast food restaurant stock price
Let T = toy company stock price

We form our first equation from the first two sentences of the word problem:
26F + 76T = 1569

The other piece of information gives us our second equation:
F = T + 27

Now, substitute “T + 27” from the second equation in the place of F in the first equation:
26*(T + 27) + 76T = 1569

Expand and combine like terms:
26T + 702 + 76T = 1569
102T + 702 – 702 = 1569 – 702
102T = 867
(1/102)* 102T = (1/102)* 867
T = $8.50

Now solve for F:
F = T + 27
F = $8.50 + $27.00 = $35.50