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brilliants [131]
3 years ago
15

Norman and Suzanne own 34 shares of a fast food restaurant stock and 70 shares of a toy company stock. At the close of the marke

ts on a particular day in​ 2004, their stock portfolio consisting of these two stocks was worth ​$1488.00. The closing price of the fast food restaurant stock was ​$30 more per share than the closing price of the toy company stock on that day. What was the closing price of each stock on that​ day?
Mathematics
1 answer:
puteri [66]3 years ago
6 0
1488=34F+70T
F=T+30
this is the system of equations heeded o solve this problem. because we are given that both stocks together are equal to $1488. we are also told that here are 34 share of the fast food stock. and there are 70 shares of the toy stock. each share has an unknown value. this is where i get the. 34F and 70T. we are told that one fast food share (F) is equal to $30 more than the toy share (T) so f=t+30.
solve he system of equations. they give you the value of f is t+30. so plug that into the original equation (1488=34F+70T) in placeof F so the new equation is 1488=34(T+30)+70T
combine like terms and solve for T. plug the value of T into the original equation and solve for F. check your work by plugging both of your answers (answer for F and answer for T) into the original equation.
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Answer:  The image of the completed table is shown below

In the completed table, we have the following values (left to right)

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  • Row Two: 15, 45, 60
  • Row Three: 45, 55, 100

==============================================

Explanation:

We're told that "40 people responded that they use mouthwash". That means we'll write "40" at the very end of the "use mouthwash" row. This represents the total number of people who use mouthwash, since we're underneath the "total" in that far right column.

Then we're further told that "Of the people who use mouthwash, 30 people use floss", so we'll write "30" in the first row, first column blank space. These are the people who both floss and use mouthwash. Because earlier we know 40 people use mouthwash overall, this leaves 40-30 = 10 people who use mouthwash, but they don't floss.

To summarize so far: In row 1, we have the following values from left to right: 30, 10, 40

The first two items of this row must add to the last item.

---------------------

Now onto row 2

Since 40 people use mouthwash, and 100 people were surveyed, this means that 100-40 = 60 people do not use mouthwash.  The value 60 goes at the very end of row 2. This represents another total.

Like earlier, the first two items must add to the last. So 40+60 = 100.

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We have 60 people who don't use mouthwash, and 45 of those people also don't floss. Therefore, 60-45 = 15 people do floss but they don't use mouthwash. We'll write "15" in the second row, first column.

Along row 2, we have the following values: 15, 45, 60

----------------------

Row 3

For each column, add up the first two items to get the third one. This will lead to the totals along this bottom row.

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The third column is already done, but again we can see that 40+60 = 100.

Furthermore, the first two items of the third row add to 45+55 = 100 which helps confirm our answers.

The full completed table is shown below.

------------------------

To summarize, we are effectively just sorting the values given to us to write them into the table. Then we use a bit of algebraic detective work to find out what values are missing so we fill out the completed table.

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