Question

Mrs. McCarthy is ordering senior portraits of her son to send to their relatives. A medium photo costs $15 and a large photo costs $42. She wants to spend less than $380 in total.
Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.
x = the number of medium photos
y = the number of large photos

Answer 1

To represent Mrs. McCarthy's situation using an inequality in standard form, we can start by translating the costs of the medium and large photos into an equation.

Let:
- \( x \) be the number of medium photos
- \( y \) be the number of large photos

The cost of medium photos is \( 15x \) (since each medium photo costs $15) and the cost of large photos is \( 42y \) (since each large photo costs $42).

Mrs. McCarthy wants to spend less than $380 in total. This can be expressed with the inequality:

\[
15x + 42y < 380
\]

To put this inequality in standard form, we typically want to have all variables on one side of the inequality and the constant on the other side. This can be done by rearranging the terms as follows:

\[
15x + 42y - 380 < 0
\]

Now the inequality \( 15x + 42y < 380 \) can also be rewritten as:

\[
15x + 42y \leq 380
\]

However, since the original question specifies "less than," the inequality remains as:

\[
15x + 42y < 380
\]

This is the standard form that describes Mrs. McCarthy's situation regarding the purchase of her son's senior portraits.