Question

At the bargain store , Tanya bought 3 items that each cost the same amount. Tony bought 5 items that each cost the same amount but each was 1.50 less than the the items that Tanya bought. both Tony and Tanya paid the same amount of money. What was the individual cost of each person's items​

Answer 1

Answer:

"Tanya bought 3 items that each cost the same amt"

"Let x represent the cost of one of Tanya's items"

  So, Tanya bought 3 items, costing x+x+x = 3x

  Note that (number of items)*(cost per item) = (number of items)*(cost/item) = cost,   [item cancels out]

 

"Tony bought 4 items that each cost the same amt, but each was $2.25 less than the items Tanya bought."

 The cost for Tony's items was:  (x-2.25)+(x-2.25)+(x-2.25)+(x-2.25) = 4*(x-2.25)

 

"Tanya and Tony paid the same amt. of money"

   This is an equation (the same amount means equals)

    Tanya's cost = Tony's cost

a.) Write an equation. Let x represent the cost of one of Tanya's items

          3x      =     4(x-2.25)

 

Now, the math:

b.) Solve the equation. Show your work.

          3x      =     4(x-2.25)

          3x  =  4x - 9.00                 [distributive principle; multiply]

         -x = -9.00                      [subtract 4x from both sides; option, could instead add 9.00, then subtract 3x from both sides, getting 9.00=x]

          x = 9.00           [multiply both sides by (-1)]

                 [note:  to "solve for x" means to find the value(s) of x that make the equation true,

                          so let's see if it is true --]

c.) Check your solution. Show your work.

  Is              3x      =     4(x-2.25), when x=9.00    ?

          3(9.00) = 4(9.00-2.25)    ?

           27.00 = 36.00 - 9.00    ?

             27.00 = 27.00    ?yes

 

d) State the solution in a complete sentence.

     The problem started with:  "Tanya bought 3 items that each cost the same amt. Tony bought 4 items that each cost the same amt, but each was $2.25 less than the items Tanya bought. Both Tanya and Tony paid the same amt. of money."

     I would write:   "Tanya bought 3 items, each costing $9.00.  Tony bought 4 items, each costing $6.75.  Tanya and Tony each paid $27.00."  

Step-by-step explanation:

Answer 2

Answer:  The required individual cost of Tanya's items is 2.25 and that of Tony's items is 3.75.

Step-by-step explanation:  Given that at the bargain store , Tanya bought 3 items that each cost the same amount.

Tony bought 5 items that each cost the same amount but each was 1.50 less than the the items that Tanya bought. both Tony and Tanya paid the same amount of money.

We are to find the individual cost of each person's items.

Let x and y represents the individual cost of Tanya's items and Tony's items respectively.

Then, according to the given information, we have

$3x=5y\\\\\Rightarrow x=\dfrac{5}{3}y~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

and

$x-1.50=y\\\\\\\Rightarrow \dfrac{5}{3}y-1.50=y~~~~~~~~~~~~~~~~~~~~~~[\textup{Using equation (i)}] \\\\\\\Rightarrow \dfrac{5}{3}y-y=1.50\\\\\\\Rightarrow \dfrac{2}{3}y=1.50\\\\\\\Rightarrow 2y=4.50\\\\\Rightarrow y=2.25.$

From equation (i), we get

$x=\dfrac{5}{3}\times2.25=3.75.$

Thus, the required individual cost of Tanya's items is 2.25 and that of Tony's items is 3.75.