I need assistance with an 8th grade algebra word problem. This is so that I can check my son's answers before he submits a unit test tomorrow. Thanks!

Question

At a bargain store,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. What was the individual cost of each person's items?

 

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

b.) Solve the equation. Show your work.

c.) Check your solution. Show your work.

d) State the solution in a complete sentence.

 

I'm a 45 year old mom who's very new to the homeschool scene. My 8th grade son has a math test tomorrow and before he submits it I'd like to be able to check it to make sure he's done his best. The only problem is, I hated word problems when I was in Jr High and I never aquired a taste for them later in life. This is the only one I haven't been able to muddle my way through. ( It could have something to do with the fact that is 4:38 am and I've yet to go to bed ) Any help would be much appreciated! You know, anything to save face and not look like a total moron to my 13 year old since he's already convinced everyone over the age of 18 is a lost cause anyway!

Answer 1

Let's see, "everyone over the age of 18" is a math word problem

.  The expression is:    x > 18 or, some might interpret it as x >= 18 for "greater than or equal to"

 

This is the translation:

 

"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."   

 

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&nbsp> My p.s.: I am now well over 18. I tell my WyzAnt students that I am not a teacher who grades you, I am a tutor -- you know, like a mentor or coach that helps you do your very best. A coach may not be able to dunk the basketball (I never could), but I can tell my 6'10" center, "I've watched game film of our opponents this week; their center is left handed and gets 16 of his regular 20 points with a fake left then a move right for his left-handed hook shot or jump shot. He is 2 inches taller than you -- you will not be able to block his shots! so, don't try !! What I want you to do is to flatten both hands and place them directly in front of his eyes (which you can reach) so he can't see the basket. I'll accept any of his luck shots."