Question

Business You manage a clothing store and budget $6000 to restock 200 shirts.
You can buy T-shirts for $12 each, polo shirts for $24 each, and rugby shirts for $36 each, If you want to have twice as many rugby shirts as polo shirts, how many of each type
of shirt should you buy?

Answer 1

Answer:

60 Polo Shirt, 20 T- Shirt, 120 Rugby Shirt

Step-by-step explanation:

T- Shirts + Polo Shirt + Rugby Shirts =200

                                 Rugby Shirts = 2( Polo Shirt)

$12(# of T- shirt) + $24( # of polo Shirts) + 36( # of Rugby Shirts) = 6000

x = number of t-shirts

y = number of polo shirts

z = number of rugby shirts

x + y + z = 200

z = 2y

12x + 24y + 36z = 6000 x + 2y + 3z = 500 {divided each side by 12}

substitute 2y, for z, into 1st and 3rd equations

x + y + 2y = 200 {substituted 2y, for z, into 1st}

x + 2y + 3(2y) = 500 {substituted 2y, for z, into 3rd}

x + 3y = 200 {combined like terms in 1st}

x + 8y = 500 {multiplied and combined like terms in 2nd}

-5y = -300 {subtracted the two equations}

y = 60 polo shirts {divided each side by -5}

z = 2y {2nd equation}

z = 2(60) {substituted 60, for y, into 2nd equation}

z = 120 rugby shirts {multiplied}

x + y + z = 200 {first equation}

x + 60 + 120 = 200 {substituted}

x + 180 = 200 {combined like terms}

-180 -180

x = 20 t-shirts {subtracted 180 from each side}

Therefore you should get 60 Polo Shirt, 20 T- Shirt, 120 Rugby Shirt.