Question

Marvin is assembling centerpieces that use candles. A small centerpiece uses 3 candles and a large centerpiece uses 5 candles. Marvin is limited to using 98 candles, the number on hand.
Write the inequality in standard form that describes this situation. Use the given numbers and the following variables.
x = the number of small centerpieces
y = the number of large centerpieces

Answer 1

To express the situation in standard form with the given variables, we start with the following:

- Let \( x \) represent the number of small centerpieces, each using 3 candles.
- Let \( y \) represent the number of large centerpieces, each using 5 candles.
- Marvin has a total of 98 candles available.

The total number of candles used can be expressed as \( 3x + 5y \). Since Marvin cannot exceed the 98 candles he has, we can write the inequality as:

\[
3x + 5y \leq 98
\]

This inequality can be considered as the equation in standard form where \( A = 3 \), \( B = 5 \), and \( C = -98 \). In standard form, we typically write the equation as:

\[
3x + 5y - 98 \leq 0
\]

However, the more common representation of the inequality would be:

\[
3x + 5y \leq 98
\]

Either of these forms is valid, but the first form is the standard form.