At the local clothing store 3 similar shirts and 4 similar jackets cost $360 and 1 shirt and 3 jacket cost $220. Find the cost of each shirt.

Question

at the local store 3 similar shirt and 4 similar jacket cost $360, and 1 shirt and 3 jacket cost $220. Find the cost of each shirts 

Answer 1

We have two situations that can be written as equations.

Three shirts and four jackets cost a total of $360.

Write that as 3S + 4J= $360

 

Next, we have one shirt and three jackets cost a total of $220

 

Write that as S + 3J= $220

 

Put the two equations together one over the other.

 

3S  +  4J   =   $360

  S  +  3J   =   $220

 

 

We want to cancel one of the unknows.

 

Lets multiply the bottom equation by three

 

now we have

3S   +   4J  =  $360      Just rewrite the top

3S    +  9J  =  $660      All terms are three times the original amount

 

Subtract the top from the bottom

 

The 3S cancels out.

We are left with    5J=$300        $300/5

 

So one jacket cost  $60

 

If jackets cost $60 then  3S   +  4J = $360

Substitute $60 for J

3S  + 4X$60  =   $360

3S   +$240    =    $360

3S   +           =    $120

So each shirt cost    ?    try      $120/3=   $40

 

Now prof you answer.

 

3X$40  +  4x$60   =   ?

$120     + $240     =  $360    OK

 

Second prof to confirm.

 

1X$40  +  3X60     =  ?

$40      +   $180    =  $220    OK, again next question, please

 

 

 

 

Answer 2

Always start off with what you know!!

 

Let x represent the cost of a shirt

Let y represent the cost of a jacket

 

Therefore,

 

3x + 4y = 360

x + 3y = 220

 

Use the second equation and solve for y.

 

x + 3y = 220

3y = 220 - x

y = (220/3) - (1/3)x

 

Now plug that in for y in the first equation.

 

3x + 4((220/3) - (1/3)x) = 360      

 

I will keep the fractions for now since it will be easier to handle as we go through the equation. 

 

Now solve for x!!

 

3x + 4((220/3) - (1/3)x) = 360

3x + (880/3) - (4/3)x = 360              Convert 360 to a fraction

3x - (4/3)x = (1080/3) - (880/3)

3x - (4/3)x = 200/3                          Convert 3 into a fraction

(9/3)x - (4/3)x = 200/3

(5/3)x = 200/3                                 Multiply each side by (3/5)

x = (200/3) x (3/5)

x = 40