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Question

Difficulty: MediumLinear Equations in One Variable

A subscription-based meal kit service charges a monthly membership fee of $35\$35 plus $8.50\$8.50 per meal. A non-member can purchase the same meals for $12.00\$12.00 each, but must pay a flat monthly delivery fee of $7\$7. How many meals must be purchased in a month for the total monthly cost for a member to be equal to the total monthly cost for a non-member?

Answer: 8 meals

Answer

The total monthly cost is equal for a member and a non-member when 8 meals are purchased in a month.
The correct answer of 8 is found by setting the member cost expression, 35+8.5m35 + 8.5m, equal to the non-member cost expression, 12m+712m + 7, and solving for the number of meals, mm.

Step-by-Step Solution

1
Represent the total monthly cost for a member and a non-member using equations where mm is the number of meals purchased.
Member cost is represented by 35+8.50m35 + 8.50m, and non-member cost is represented by 12.00m+712.00m + 7.
To set up an algebraic representation of the cost structures.
2
Equate the two cost expressions to find the number of meals where the costs are equal.
35+8.50m=12.00m+735 + 8.50m = 12.00m + 7
To find the value of mm that makes both costs equivalent.
3
Isolate the variable mm on one side of the equation.
3.50m=283.50m = 28
Subtracting 8.50m8.50m and 77 from both sides simplifies the equation by keeping variable terms on one side and constants on the other.
4
Divide both sides of the equation by 3.503.50 to solve for mm.
m=8m = 8
Dividing 2828 by 3.503.50 yields the final number of meals.

Key Concept

Solving linear equations in one variable with variable terms on both sides of the equation
Estimated Time:1m 30s
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Topics

Linear Equations in One Variable

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