Erik wants to save some low-resolution photos and some high-resolution photos on his flash drive. Each low-resolution photo takes up $1\,\text{MB}$ and each high-resolution photo takes up $4\,\text{MB}$ . In total, they cannot exceed the total storage space available on the drive, which is $1,970\,\text{MB}$ . $\newline$ Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. $\newline$ $x =$ the number of low-resolution photos $\newline$ $y =$ the number of high-resolution photos $\newline$ $\newline$ Choices: $\newline$ (A) $4 + x + 1 + y \leq 1,970$ $\newline$ (B) $x + 4y \leq 1,970$ $\newline$ (C) $1 + x + 4 + y \leq 1,970$ $\newline$ (D) $4x + y \leq 1,970$

Full solution

Q. Erik wants to save some low-resolution photos and some high-resolution photos on his flash drive. Each low-resolution photo takes up

1\,\text{MB}

and each high-resolution photo takes up

4\,\text{MB}

. In total, they cannot exceed the total storage space available on the drive, which is

1,970\,\text{MB}

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of low-resolution photos

\newline

y =

the number of high-resolution photos

\newline

\newline

Choices:

\newline

(A)

4 + x + 1 + y \leq 1,970

\newline

(B)

x + 4y \leq 1,970

\newline

(C)

1 + x + 4 + y \leq 1,970

\newline

(D)

4x + y \leq 1,970

Define Variables: Define the variables in terms of the problem's context. We are given that $x$ represents the number of low-resolution photos and $y$ represents the number of high-resolution photos. Each low-resolution photo takes up $1\,\text{MB}$ and each high-resolution photo takes up $4\,\text{MB}$ .
Low-Resolution Storage: Write an expression for the total storage used by the low-resolution photos. Since each low-resolution photo takes up $1\,\text{MB}$ , the total storage for $x$ low-resolution photos is $1\times x$ or simply $x\,\text{MB}$ .
High-Resolution Storage: Write an expression for the total storage used by the high-resolution photos. Since each high-resolution photo takes up $4\,\text{MB}$ , the total storage for $y$ high-resolution photos is $4*y$ or $4y\,\text{MB}$ .
Total Storage: Combine the expressions from Step $2$ and Step $3$ to get the total storage used by both types of photos. This gives us $x + 4y$ MB as the total storage used.
Total Storage Inequality: We know that the total storage used by both types of photos cannot exceed the total storage space available on the drive, which is $1,970$ MB. Therefore, the inequality that represents this situation is $x + 4y \leq 1,970$ .
Match with Choices: Match the inequality from Step $5$ with the given choices. The correct inequality that matches is $(B) x + 4y \leq 1,970$ .