Question

Patricia can buy individual songs for $1.00 to download. Also, an entire album costs $10.00 to download. She can spend no more than a total of $80. She wants to buy no more than four albums, and at least 30 individual songs. The following system of inequalities represents this situation, where x is the number of individual songs and y is the number of albums.

x plus 10 y less or equal than 80
x greater or equal than 30
y less or equal than 4


Which yellow shaded region corresponds to Patricia’s possible choices?

Answer 1

The region of possible choices is the area of the xy-plane where all restrictions are satisfied, and is shaded in the picture attached.

Explanation:

We have 3 restrictions, plus the condition that both x and y are positive.

The region of possible choices is the area of the xy-plane where all restrictions are satisfied.

The restrictions are:

`x+10y\leq80\\\\x\geq30\\\\y\leq4`

Then we can graph all the restrictions in paper or software.

In the figure attached we have shaded in yellow the region of possible values.