Tisha is investing in the stock market and has a maximum budget of $4,400 with which to purchase stock in two promising companies. Stock in the software company currently sells for $12 per share. Stock in the robotics company is currently trading at $44 per share.

Question

Write the inequality in standard form that describes this situation. Use the given numbers and the following variables.
x = the number of shares in the software company
y = the number of shares in the robotics company

Answer 1

To write the inequality that describes Tisha's investment situation in standard form, we can analyze the problem as follows:

1. The cost of shares in the software company is $12 per share, so if Tisha buys \( x \) shares, her total cost for the software company will be \( 12x \).

2. The cost of shares in the robotics company is $44 per share, so if Tisha buys \( y \) shares, her total cost for the robotics company will be \( 44y \).

3. Tisha has a maximum budget of $4,400 for her investments. Therefore, the total cost of the shares must be less than or equal to her budget:

\[ 12x + 44y \leq 4400 \]

To express this inequality in standard form (Ax + By ≤ C), we can rearrange it if needed. The inequality is already close to standard form, but we typically rewrite it by dividing through by 4 to simplify:

\[ 3x + 11y \leq 1100 \]

Thus, the final inequality in standard form is:

\[ 3x + 11y \leq 1100 \]