Question
You have the choice between two grocery delivery services. Door Drop charges an \( \$ 11 \) fee plus \( 13 \% \) of the cost of the groceries. Fresh Food charges a \( \$ 15 \) fee plus \( 11 \% \) of the cost of the groceries. (a) Write an equation to express the cost \( y \) in dollars for the delivery of \( x \) dollars of groceries by Door Drop. (b) Write an equation to express the cost \( y \) in dollars for the delivery of \( x \) dollars of groceries by Fresh Food. (c) What is the amount of groceries for which both companies charge the same delivery fee? How much is the fee? (a) Write an equation to express the cost \( y \) in dollars for the delivery of \( x \) dollars of groceries by Door Drop \( \square \) (Do not include the \( \$ \) symbol in your answer. Use integers or decimals for any numbers in the equation.) (b) Write an equation to express the cost y in dollars for the delivery of x dollars of groceries by Fresh Food. \( \square \) (Do not include the \( \$ \) symbol in your answer Use integers or decimals for any numbers in the equation.) (c) The amount of groceries for which both companies charge the same delivery fee is \( \$ \) \( \square \) The fee is \( \$ \) \( \square \) (iype integers or decimals.)
Ask by Bates Young. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
(a) \( y = 11 + 0.13x \)
(b) \( y = 15 + 0.11x \)
(c) Both companies charge the same fee when the grocery cost is \$200, and the fee is \$37.
Solution
(a) For Door Drop, the cost is the flat fee plus \( 13\% \) of the grocery cost:
\[
y = 11 + 0.13x
\]
(b) For Fresh Food, the cost is the flat fee plus \( 11\% \) of the grocery cost:
\[
y = 15 + 0.11x
\]
(c) To find the amount of groceries where both companies charge the same fee, set the two equations equal:
\[
11 + 0.13x = 15 + 0.11x
\]
Subtract \( 0.11x \) from both sides:
\[
11 + 0.02x = 15
\]
Subtract \( 11 \) from both sides:
\[
0.02x = 4
\]
Divide both sides by \( 0.02 \):
\[
x = 200
\]
Now substitute \( x = 200 \) into one of the equations (using Door Drop's equation):
\[
y = 11 + 0.13(200) = 11 + 26 = 37
\]
The amount of groceries for which both companies charge the same delivery fee is \( 200 \) and the fee is \( 37 \).
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Extra Insights
(a) \( y = 11 + 0.13x \) (b) \( y = 15 + 0.11x \) (c) The amount of groceries for which both companies charge the same delivery fee is \( 43.75 \). The fee is \( 16.75 \). To find the amount of groceries where both delivery services charge the same, set the two equations equal to each other: \[ 11 + 0.13x = 15 + 0.11x. \] Solving for \( x \) gives \( x = 43.75 \). Plugging this back into either equation results in a delivery fee of \( 16.75 \).
