pam sells handwoven rugs through an online store for $50 each. she spent $98 on weaving equipment, and she…
pam sells handwoven rugs through an online store for $50 each. she spent $98 on weaving equipment, and she spends $38.20 on materials for each rug. additionally, the online store charges pam $4.80 to ship each rug. which equation can you use to find r, the number of rugs pam must sell for her sales to equal her expenses? 50r + 4.8 = 38.2r + 98 50r = 98 + 38.2r + 4.8r how many rugs must pam sell for her sales to equal her expenses? rugs
Answer
Explanation:
Step1: Set up the cost - revenue equation
Revenue from selling $r$ rugs at $50$ dollars each is $50r$. The fixed cost is $98$ (for weaving equipment), and the variable cost per rug is the sum of material cost ($38.20$) and shipping cost ($4.80$), so the total variable cost for $r$ rugs is $(38.2 + 4.8)r=43r$. The total cost is $98 + 43r$. We set revenue equal to cost: $50r=98 + 38.2r+4.8r$.
Step2: Solve the equation for $r$
First, simplify the right - hand side of the equation: $50r=98 + 43r$. Then, subtract $43r$ from both sides: $50r-43r=98+43r - 43r$. This gives $7r = 98$.
Step3: Isolate $r$
Divide both sides of the equation $7r = 98$ by $7$: $r=\frac{98}{7}=14$.
Answer:
14