you are choosing between two plans at a discount warehouse. plan a offers an annual membership of $50 and…

you are choosing between two plans at a discount warehouse. plan a offers an annual membership of $50 and you pay 10% of the manufacturers recommended list price. plan b offers an annual membership fee of $30 and you pay 30% of the manufacturers list price.\na. express the total yearly amount paid to the warehouse under plan a, f, as a function of the dollars of merchandise purchased during the year, x.\nf(x)=50 + 0.1x (use integers or decimals for any numbers in the expression.)\nb. express the total yearly amount paid to the warehouse under plan b, g, as a function of the dollars of merchandise purchased during the year, x.\ng(x)=30 + 0.3x (use integers or decimals for any numbers in the expression.)\nc. how many dollars of merchandise would you have to purchase in a year to pay the same amount under both plans? what will be the total yearly amount paid to the warehouse for each plan?\ndollars of merchandise = $□ (simplify your answer.)

you are choosing between two plans at a discount warehouse. plan a offers an annual membership of $50 and you pay 10% of the manufacturers recommended list price. plan b offers an annual membership fee of $30 and you pay 30% of the manufacturers list price.\na. express the total yearly amount paid to the warehouse under plan a, f, as a function of the dollars of merchandise purchased during the year, x.\nf(x)=50 + 0.1x (use integers or decimals for any numbers in the expression.)\nb. express the total yearly amount paid to the warehouse under plan b, g, as a function of the dollars of merchandise purchased during the year, x.\ng(x)=30 + 0.3x (use integers or decimals for any numbers in the expression.)\nc. how many dollars of merchandise would you have to purchase in a year to pay the same amount under both plans? what will be the total yearly amount paid to the warehouse for each plan?\ndollars of merchandise = $□ (simplify your answer.)

Answer

Explanation:

Step1: Set the two functions equal

Set (f(x)=g(x)), so (50 + 0.1x=30+0.3x).

Step2: Move the (x) - terms to one side

Subtract (0.1x) from both sides: (50=30 + 0.3x-0.1x), which simplifies to (50=30 + 0.2x).

Step3: Move the constant to the other side

Subtract 30 from both sides: (50 - 30=0.2x), so (20 = 0.2x).

Step4: Solve for (x)

Divide both sides by 0.2: (x=\frac{20}{0.2}=100).

Answer:

100