Applications of linear equations

Question

The total cost of a belt and a sweater was . If the price of the belt was less than the sweater, what was the price of the belt? Express your answer as a simplified fraction or a decimal rounded to two places.

Answer 1

B + S = T = total cost of both Belt and Sweater

B<S

B = S- x

S = B+x

where x= difference in price between Belt & Sweater

S-x + S = T

2S = T+x

S = T/2 + x/2 = the Sweater price= half the Total price plus half the difference in price

S = (T+x)/2

B +B+x = T

2B = T-x

B = T/2 -x/2 = the Belt price = half the Total price minus half the difference in prices

B = (T-x)/2