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A shopkeeper paid $9 380 for some shirts and jeans.He bought 4 times as many shirts as jeans.Each pair of jeans cost $40 more than a shirt.He paid $3 836 more for the shirts than the jeans.Find the cost of a pair of jeans.

Guest Aug 11, 2014

Best Answer 

 #1
avatar+78744 
+10

Let x be the total cost of the jeans

And since the shopkeeper paid $3836 more for the shirts than the jeans, we have

x + x + 3836 = 9380

$2772 = x = total cost of the jeans

2772 + 3836 = $6608 = total cost of shirts

 Let y = number of jeans bought

Let p + 40 = price of one pair of jeans

Let 4y = number of shirts bought

Let p = price of each shirt

So we have that the price of a pair of jeans times the number he bought  = $2772.. or...

(p + 40)y = 2772

And, solving for y, we have

y = 2772/(p + 40)     

And the price of each shirt times the number he bought = $6608...or.....

p(4y) =  6608

And substituting in for y and solving for p, we have

4p[2772/(p + 40)] = 6608     (multiply both sides by p + 40 )

11088p = 6608p + 264320

4480p = 264320

p = $59  =  cost of each shirt

p + 40 = $99   =  cost of a pair of jeans

Now, to find the number of pairs of jeans bought, we have, the price of each pair times the number purchased = $2772....or......

$99y = $2772     solve for y

y = 28  = number of pairs of jeans bought

And he bought 4 times as many shirts, so... 4y = 4(28) = 112 = number of shirts bought

Verifying our answers

28($99) + 112($59) = $9380 = the total cost

So....$99 for each pair of jeans seems correct....

 

CPhill  Aug 11, 2014
Sort: 

1+0 Answers

 #1
avatar+78744 
+10
Best Answer

Let x be the total cost of the jeans

And since the shopkeeper paid $3836 more for the shirts than the jeans, we have

x + x + 3836 = 9380

$2772 = x = total cost of the jeans

2772 + 3836 = $6608 = total cost of shirts

 Let y = number of jeans bought

Let p + 40 = price of one pair of jeans

Let 4y = number of shirts bought

Let p = price of each shirt

So we have that the price of a pair of jeans times the number he bought  = $2772.. or...

(p + 40)y = 2772

And, solving for y, we have

y = 2772/(p + 40)     

And the price of each shirt times the number he bought = $6608...or.....

p(4y) =  6608

And substituting in for y and solving for p, we have

4p[2772/(p + 40)] = 6608     (multiply both sides by p + 40 )

11088p = 6608p + 264320

4480p = 264320

p = $59  =  cost of each shirt

p + 40 = $99   =  cost of a pair of jeans

Now, to find the number of pairs of jeans bought, we have, the price of each pair times the number purchased = $2772....or......

$99y = $2772     solve for y

y = 28  = number of pairs of jeans bought

And he bought 4 times as many shirts, so... 4y = 4(28) = 112 = number of shirts bought

Verifying our answers

28($99) + 112($59) = $9380 = the total cost

So....$99 for each pair of jeans seems correct....

 

CPhill  Aug 11, 2014

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