Question

You go shopping at a local department store with your friend and cousin. You buy one pair of jeans, four pairs of shorts, and two shirts for $84. Your friend buys two pairs of jeans, one pair of shorts and three shirts for $76. Your cousin buys one pair of jeans, two pairs of shorts and one shirt for $52. Find the cost of one pair of shorts.​

Answer 1

So, cost of 1 pair of shorts =$12

Explanation:

Let cost of 1 pair of jeans =x

Cost 1pair of shorts =y

cost of 1 pair of shirts=z

We can set up equations as

x+4 y+2 z=84

2 x+1 y+3 z=76

x+2 y+z=52

Solve the equations for y.

Take first and second equations multiply first equation by -2 and add it with second equation.

-2 x-8 y-4 z=-168

2 x+1 y+3 z=76

Add them, it gives -7 y-z =-92

Now, take second and third equations, multiply the third equation by -2 then add them together.

2 x +1 y +3 z =76

-2 x-4 y-2 z=-104

Add them together,

-3 y +z =-28

Now, take the -7 y -z =-92 and -3 y +z =-28

Add the equations

-10 y = -120

Divide both sides by -10

y =12.

So, cost of 1 pair of shorts =$12

z=8