Sophia is going to purchase some writing instruments at the school store, where mechanical pencils cost $1 and pens cost $2. She can spend up to $15, but not more.

Question

Write the inequality in standard form that describes this situation. Use the given numbers and the following variables.
x = the number of mechanical pencils Sophia will buy
y = the number of pens Sophia will buy

Answer 1

To set up the inequality in standard form, we start by noting the costs of the writing instruments and the maximum amount Sophia can spend.

Let:

• \( x \) = the number of mechanical pencils (costing $1 each)
• \( y \) = the number of pens (costing $2 each)

The total cost for the mechanical pencils is \( 1x \) (since each mechanical pencil costs $1) and the total cost for the pens is \( 2y \) (since each pen costs $2).

Since Sophia can spend up to $15, we write the inequality that represents this situation:

\[ 1x + 2y \leq 15 \]

To express this in standard form, we rearrange the inequality as follows:

\[ x + 2y \leq 15 \]

Thus, the inequality in standard form that describes Sophia's spending on mechanical pencils and pens is:

\[ x + 2y \leq 15 \]