. Maria Sold Lemonade For $5 A Cup. She Spent $25 On Supplies. Antonio Sold Lemonade For $4 A Cup. Write An Inequality That Shows C, The Number Of Cups Of Lemonade Have To Be Sold In Order For Antonio To Make At Least As Much As Maria.
Maria and Antonio's Lemonade Stand: A Math Problem
In this article, we will explore a math problem involving two friends, Maria and Antonio, who run a lemonade stand. Maria sells lemonade for $5 a cup, while Antonio sells lemonade for $4 a cup. Maria spends $25 on supplies, while Antonio's expenses are not specified. We will write an inequality that shows the number of cups of lemonade Antonio needs to sell in order to make at least as much as Maria.
Maria sells lemonade for $5 a cup, and she spends $25 on supplies. This means that Maria's revenue is $5c, where c is the number of cups of lemonade she sells. Her total earnings are $5c - $25. Antonio sells lemonade for $4 a cup, and we want to find the number of cups of lemonade he needs to sell in order to make at least as much as Maria.
Let's denote the number of cups of lemonade Antonio sells as x. Then, Antonio's revenue is $4x, and his total earnings are $4x - $25 (assuming he also spends $25 on supplies). We want to find the value of x such that Antonio's earnings are at least as much as Maria's earnings. This can be written as an inequality:
$4x - $25 ≥ $5c - $25
We can simplify the inequality by adding $25 to both sides:
$4x ≥ $5c
To isolate c, we can divide both sides of the inequality by 4:
c ≤ $4x / 5
The inequality c ≤ $4x / 5 shows that the number of cups of lemonade Maria sells (c) is less than or equal to $4x / 5, where x is the number of cups of lemonade Antonio sells. This means that Antonio needs to sell at least $4x / 5 cups of lemonade in order to make at least as much as Maria.
Let's say Antonio sells 10 cups of lemonade. Then, x = 10, and we can plug this value into the inequality:
c ≤ $4(10) / 5 c ≤ $8
This means that Maria needs to sell at most 8 cups of lemonade in order for Antonio to make at least as much as her.
In this article, we wrote an inequality that shows the number of cups of lemonade Antonio needs to sell in order to make at least as much as Maria. The inequality is c ≤ $4x / 5, where x is the number of cups of lemonade Antonio sells. We also provided an example to illustrate how to use the inequality in a real-world scenario.
Maria and Antonio's Lemonade Stand: A Math Problem - Q&A
In our previous article, we explored a math problem involving two friends, Maria and Antonio, who run a lemonade stand. Maria sells lemonade for $5 a cup, while Antonio sells lemonade for $4 a cup. Maria spends $25 on supplies, while Antonio's expenses are not specified. We wrote an inequality that shows the number of cups of lemonade Antonio needs to sell in order to make at least as much as Maria. In this article, we will answer some frequently asked questions about the problem.
A: The inequality is used to determine the number of cups of lemonade Antonio needs to sell in order to make at least as much as Maria. It helps us understand the relationship between the number of cups of lemonade sold by Maria and Antonio.
A: We divide by 4 because the inequality is in the form $4x ≥ $5c. To isolate c, we need to get rid of the 4 on the left-hand side of the inequality. Dividing both sides by 4 achieves this.
A: No, we cannot assume that Antonio's expenses are the same as Maria's. The problem states that Maria spends $25 on supplies, but it does not specify Antonio's expenses. However, for the sake of the problem, we assumed that Antonio also spends $25 on supplies.
A: If Antonio sells more than 10 cups of lemonade, then x > 10. Plugging this value into the inequality, we get:
c ≤ $4(10) / 5 c ≤ $8
However, since x > 10, we know that c must be less than $8. This means that Maria needs to sell fewer than 8 cups of lemonade in order for Antonio to make at least as much as her.
A: Yes, we can use this inequality to compare the earnings of Maria and Antonio. The inequality shows that Antonio needs to sell at least $4x / 5 cups of lemonade in order to make at least as much as Maria. This means that if Antonio sells more than $4x / 5 cups of lemonade, then he will make more than Maria.
A: If Maria sells more than 8 cups of lemonade, then c > 8. Plugging this value into the inequality, we get:
c ≤ $4x / 5 c ≤ $4(8) / 5 c ≤ $6.4
However, since c > 8, we know that c must be greater than $6.4. This means that Maria needs to sell more than 6.4 cups of lemonade in order for Antonio to make at least as much as her.
In this article, we answered some frequently asked questions about the math problem involving Maria and Antonio's lemonade stand. We explained the purpose of the inequality, why we need to divide by 4, and how to use the inequality to compare the earnings of Maria and Antonio. We also provided examples to illustrate how to use the inequality in different scenarios.