Answer to Question #265925 in Algebra for Doc

Question

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.

Answer 1

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

$$C_1=3x$$

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

$$C_2=5y$$

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

$$C_3=2z$$

Now, translate to math language the following phrases.

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

$$x=2y.$$

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

$$z=300+y.$$

The athlete hands the cashier $ 1380:

$$C_1+C_2+C_3=1380,\\ 3x+5y+2z=1380.$$

Substitute equation 1 and equation 2 into the last equation:

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