Kristin spent $131 on shirts. Fancy shirts cost $28 and plain shirts cost $15. If she bought a total of 7 then how many of each kind did she buy?

Question

I need to know how to do this problem, and the steps to do it.

Answer 1

Hi Chrissa,

 

The trick to this type of problem is turning the word problem into a set of equations that we can solve.  There are two unknowns (how many fancy shirts she bought and how many plain shirts she bought), so we know that we will need two equations to solve this problem.

 

Let's first cover the equation that will relate the number of both types of shirts she bought and the price of each type of shirt to the total price she paid and define some variables that we will use to represent those unknown values:

 

Let's use the variable F for the number of fancy shirts that she bought and P for the number of plain shirts that she bought.

 

From our knowledge, we know that if we buy five shirts that each cost $1, we will spend a total ($1)x5=$5, so we can use that to create our first equation:

 

($28)x(F)+($15)x(P)=$131 (the total she spent on shirts)

 

Now we have to think about what else we know about the problem to get another equation.  Well, we know that she bought a total of 7 shirts, so we can use that to make our last equation:

 

F+P=7  (the number of fancy shirts bought plus the number of plain shirts bought is equal to 7 shirts)

 

Now that we have 2 equations an 2 unknowns, we can use a suitable method for solving systems of equations.  I would recommend substitution.  In substitution, we solve for one of our variable in one equation and substitute it in for the same variable in the other equation:

 

F+P=7

 

F+P-P=7-P  (subtract P from both sides)

 

F=7-P (combine like terms)

 

Now substitute the right side of that equation into F of our first equation:

 

($28)xF+($15)xP=$131

 

(28)x(7-P)+15P=$131 (substitute for F)

 

28x7-28P+15P=$131  (distribute)

 

196-13P=$131 (multiplication and combine like terms)

 

196-13P+13P=$131+13P (add 13P to both sides)

 

196=131+13P (combine like terms)

 

196-131=131-131+13P (subtract 131 from both sides)

 

65=13P (combine like terms)

 

65/13=13P/13 (divide both sides by 13 to solve for P)

 

5=P (division and cancellation of numerator and denominator)

 

We have solved for P (the number of plain shirts that she bought) This is a good sign, as it is a positive whole number.  (We can't buy -0.554 shirts)

 

Now we can plug this value into our second equation to easily get F (the number of fancy shirts that she bought).

 

F+P=7

 

F+5=7 (substitute for P)

 

F+5-5=7-5 (subtract 5 from both sides)

 

F=2 (combine like terms)

 

We have now solved for F (the number of fancy shirts that she bought).

 

These two solution can be check by substituting both values of F and P into our first equation and making sure that we get $131 for the total.

 

 

 

I hope that my explanation cleared up anything that you didn't fully understand about the problem.  The trickiest part is coming up with the equations from the word problem.  And always remember that you need an equation for each unknown that you have.  If you have any further questions, feel free to ask.

 

Best regards,

 

Josh

Answer 2

The key to any story problem is to define variables. 

Let f= number of fancy shirts

Let p= number of plain shirts

Then

   28f= $ cost of fancy shirts

   15p= $ cost of plain shirts

Consider the problem states the purchase totaled: 7 shirts and $131

Use these to set up two equations,

One for number, one for $

So f+p=7 and 28f+15p=131

Now solve this system of equations by either substitution (the easier for this pair), or cancellation.

Note how easy translation from story problem to math is if you carefully define your variables, then use the data from the story to create equations.  

If solving a system of equations is your difficulty, get back with that question.