Question #265925

An athlete buys three T-shirts, five sweat-bands and two pairs of running shoes from a sports outlet.

A T-shirt costs twice as much as a sweat-band, while a pair of running shoes costs $ 300 more than a

sweat-band. The athlete hands the cashier $ 1380

Determine the cost of a T-shirt, a sweat-band and a pair of running shoes.


1
Expert's answer
2021-11-15T16:11:56-0500

Three T-shirts cost (the cost of each is x):


C1=3xC_1=3x

Five sweat-bands cost (the cost of each is y):


C2=5yC_2=5y

Two pairs of running shoes (the cost of a pair is z):


C3=2zC_3=2z



Now, translate to math language the following phrases.

A T-shirt costs twice as much as a sweat-band (equation 1):


x=2y.x=2y.

A pair of running shoes costs $ 300 more than a sweat-band (equation 2):


z=300+y.z=300+y.

The athlete hands the cashier $ 1380:


C1+C2+C3=1380,3x+5y+2z=1380.C_1+C_2+C_3=1380,\\ 3x+5y+2z=1380.

Substitute equation 1 and equation 2 into the last equation:


3(2y)+5y+2(300+y)=1380,6y+5y+600+2y=1380,13y+600=1380,13y=780,y=60. x=2y=260=120,z=300+y=300+60=360.3(2y)+5y+2(300+y)=1380,\\ 6y+5y+600+2y=1380,\\ 13y+600=1380,\\ 13y=780,\\ y=60.\\\space\\ x=2y=2·60=120,\\ z=300+y=300+60=360.


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