Final answer:
Using algebra, we determine that Rachel sold $100, Barb sold $60, and Yohanna sold $160 by setting up and solving a system of equations based on their combined sales and the amounts each sold relative to the others.
Step-by-step explanation:
The subject of this question is Mathematics, specifically algebraic word problems that require setting up and solving a system of equations. We are given a scenario involving Rachel, Barb, and Yohanna, who work in a clothing shop and have combined sales of $320.
We can start by translating the word problem into algebraic expressions based on the information given:
- Rachel sold $40 more than Barb, so we have the equation r = b + $40.
- Altogether, Barb and Yohanna sold $120 more than Rachel, giving us the equation b + y = r + $120.
- The total sales by all three is $320, which gives us r + b + y = $320.
Using these equations, we can solve for the individual amounts each person sold.
- Substitute r from the first equation into the second equation to get b + y = b + 40 + 120.
- Simplify to find Yohanna's sales: b + y = b + 160, which simplifies to y = 160.
- Substitute y = 160 and r = b + 40 into the third equation and solve for b.
- r + b + 160 = 320, which simplifies to r + b = 160. Then b + 40 + b = 160, so 2b + 40 = 160.
- Solve for b to find b = $60.
- Finally, calculate r: r = b + 40, so r = $100.
In conclusion, Rachel sold $100, Barb sold $60, and Yohanna sold $160.