Colin is purchasing chocolate truffles to use as party favors. To ensure there are enough for everyone, he needs to purchase at least 169 pieces. Dark chocolate truffles come in boxes of 9 pieces and milk chocolate truffles come in boxes of 28 pieces.

Question

Write the inequality in standard form that describes this situation. Use the given numbers and the following variables.
x = the number of boxes of dark chocolate truffles
y = the number of boxes of milk chocolate truffles

Answer 1

To represent the situation in standard form using the given variables, we need to create an inequality based on the quantities of chocolate truffles Colin is purchasing.

1. Understand the problem:

   • Each box of dark chocolate truffles contains 9 pieces.
   • Each box of milk chocolate truffles contains 28 pieces.
   • Colin needs at least 169 truffles in total.

2. Translate the quantities into the inequality:

   • The total number of truffles from dark chocolate boxes is \(9x\) (where \(x\) is the number of boxes of dark chocolate).
   • The total number of truffles from milk chocolate boxes is \(28y\) (where \(y\) is the number of boxes of milk chocolate).

3. Set up the inequality:

   • The total number of truffles must be at least 169, so we write: \[ 9x + 28y \geq 169 \]

4. Standard Form:

   • The standard form of a linear inequality is usually written as: \[ Ax + By \geq C \] where \(A\), \(B\), and \(C\) are constants, and \(A\) and \(B\) are non-negative. In this case, the inequality is already in standard form: \[ 9x + 28y \geq 169 \]

Thus, the inequality that describes the situation in standard form is:

\[ 9x + 28y \geq 169 \]