Question 185003
1. Define variables:
w = price of a sweater, in dollars
h = price of a shirt, in dollars

2. Set up two equations representing the problem:
{{{w = 2h - 5}}}
{{{4h + 3w = 275}}}

3. Since an equation for one variable is solved, substitute the answer for the variable in the other equation:
{{{4h + 3(2h - 5) = 275}}}

4. Distribute the 3:
{{{4h + 6h - 15 = 275}}}

5. Combine two terms:
{{{10h - 15 = 275}}}

6. Add 15 to both sides:
{{{10h - 15 + 15 = 275 + 15}}}

7. Cancel and combine terms:
{{{10h = 290}}}

8. Divide both sides by 10:
{{{(10h)/10 = 290/10}}}

9. Finish simplification:
{{{h = 29}}}

10. Replace h in your first equation:
{{{w = 2(29) - 5}}}

11. Solve for w:
{{{w = 58 - 5}}}
{{{w = 53}}}

12. Combine your solved equations with your variable definitions for your answer:
A shirt costs $29 and a sweater costs $53.