Question

James bought two T-shirts and one pair of jeans at an online store and paid $40, not including taxes, for his purchase. A month later, the same store

sold the T-shirts and jeans at a 50% discount from their original prices. James bought two T-shirts and five pairs of jeans for $60, not including taxes.
and
Assuming the base prices of the T-shirts and the jeans are the same on both occasions, and ignoring the taxes, the price of a T-shirt is $
the price of a pair of jeans is $

Answer 1

`\boxed{\text{\$10; \$20}}`

Explanation:

Let t = the price of a T-shirt

and j = the price of a pair of jeans

You have a system of two equations:

`\begin{cases}(1)& 2t + j = 40\\(2) & 2(0.5t) + 5(0.5j) = 60\end{cases}\\`

`\begin{array}{lrcll}(3) & t+ 2.5j & = & 60 &\text{Removed parentheses in (2)}\\(4)& 2t + 5j & = & 120 &\text{Multiplied (3) by 2}\\& 4j & = & 80 &\text{Subtracted (4) from (1)}\\(5)& j & = & 20 &\text{Divided each side by 4} \\& 2t + 20& = & 40 & \text{Substituted (5) into (1)} \\&2t & = & 20 & \text{Subtracted 20 from each side}\\& t & = & 20 & \text{Divided each side by 2}\\\end{array}`

`\text{The price of a T-shirt is \boxed{\textbf{\$10}}}\\\\\text{and the price of a pair of jeans is \boxed{\textbf{\$20}}}\\`

Check:

`\begin{array}{rclcrcl}2*10\ + 20 & = & 40 & \qquad &2(0.5*10) + 5(0.5*20)&=&60\\20 + 20 & = & 40 & \qquad &2*5 + 5* 10& = &60\\40& = & 40 &\qquad &10 + 50 & = & 60\\& & &\qquad &60 & = & 60\\\end{array}`

OK.