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.

Answer 1

The system of inequalities is:

`x\geq30\\\\y\leq4\\\\10x+1y\leq80`

Explanation:

We will write each of the conditions stated in this problem

Patricia wants to buy at least 30 individual songs.

`x\geq30`

She wants to buy 4 albums at most.

`y\leq4`

The total expenditure has to be equal or less than $80, when each album cost $10 and each individual song cost $1.

`10x+1y\leq80`

The system of inequalities is:

`x\geq30\\\\y\leq4\\\\10x+1y\leq80`