Cathy makes two different types of candy: truffles and jellybeans. She charges $9
a box for the truffles and $6 a box for the jellybeans. If she decides to make 28
boxes of candy one day, what is the minimum number of boxes of truffles she
should make if she is to gross at least $216? [Only algebraic solutions will receive
credit.]
j = 28 - t
9t + 6j = 9t + 6(28-t) = 9t + 168 - 6t = 216
Solve for t.
16
Well, Cathy is in a bit of a sticky situation, isn't she? She wants to make some money selling candy, but she needs to make sure she meets her goal of at least $216 in gross revenue. Let's see what we can do to help her out.
Let's say Cathy makes x boxes of truffles. Since she wants to make a minimum of $216, we can set up an equation:
9x + 6(28 - x) ≥ 216
Here's the breakdown: Cathy charges $9 per box for the truffles, so she'll make 9x dollars from the truffle boxes. She's making a total of 28 boxes of candy, so she subtracts x from 28 to find how many jellybean boxes she should make (28 - x). Each jellybean box sells for $6, so she'll make 6(28 - x) dollars from those.
Now, let's solve the equation:
9x + 6(28 - x) ≥ 216
9x + 168 - 6x ≥ 216
3x + 168 ≥ 216
3x ≥ 48
x ≥ 16
So, the minimum number of boxes of truffles Cathy should make is 16 if she wants to gross at least $216.
Now, let's hope her truffles are as sweet as her success!
To find the minimum number of boxes of truffles Cathy should make, we can set up an algebraic equation based on the given information.
Let's represent the number of boxes of truffles Cathy makes as 'x'.
According to the problem, she also makes 28 boxes of candy in total.
Since each box of truffles costs $9, the total revenue from truffles is 9 * x = 9x dollars.
Similarly, since each box of jellybeans costs $6, the total revenue from jellybeans would be (28 - x) * 6 = 168 - 6x dollars.
To find the minimum number of boxes of truffles Cathy should make, we need to determine the value of 'x' that satisfies the condition of grossing at least $216.
So, we can set up the equation:
Total revenue from truffles + Total revenue from jellybeans ≥ $216
9x + (168 - 6x) ≥ 216
Simplifying the equation:
9x + 168 - 6x ≥ 216
3x + 168 ≥ 216
3x ≥ 216 - 168
3x ≥ 48
x ≥ 16
Therefore, the minimum number of boxes of truffles Cathy should make is 16.
To find the minimum number of boxes of truffles Cathy should make, we can set up an algebraic equation.
Let's say the number of boxes of truffles Cathy makes is 'x'. Since she makes a total of 28 boxes of candy, the number of boxes of jellybeans she makes would be (28 - x).
Cathy charges $9 for each box of truffles, so the total revenue from the truffles would be 9x. Similarly, she charges $6 for each box of jellybeans, so the total revenue from the jellybeans would be 6(28 - x).
According to the problem, Cathy wants to gross at least $216. Therefore, we can set up the following inequality:
9x + 6(28 - x) ≥ 216
Now, let's solve the inequality to find the minimum number of boxes of truffles Cathy should make:
9x + 168 - 6x ≥ 216
3x + 168 ≥ 216
3x ≥ 216 - 168
3x ≥ 48
x ≥ 48/3
x ≥ 16
Therefore, Cathy should make at least 16 boxes of truffles in order to gross at least $216.