A company buys paper at the rate of $10.50 per package for the first 10 packages, $8.50 per package for the next 10 packages, and $5.50 per package for any additional packages. How many packages of paper can be bought for $322.00?

The company uses three rates to determine the amount of purchase they procure. When the three rates are put into consideration, the total number of papers that can be bought for $3200 is 44 packages .

Given that:

[tex]Rate_1= \$10.50[/tex] for first 10

[tex]Rate_2 = \$8.50[/tex] for the next 10

[tex]Rate_3 = \$5.50[/tex] for additional

[tex]Amount = \$322.00[/tex]

Represent the additional package with x.

The equation that amounts to $322.00 is:

[tex]Amount = Rate_1 \times 10 + Rate_2 \times 10 + Rate_3 \times x[/tex]

So, we have:

[tex]322.00 = 10.50\times 10 + 8.50\times 10 + 5.50\times x[/tex]

[tex]322.00 = 105.0 + 85.0 + 5.50\times x[/tex]

Collect like terms

[tex]322.00 - 105.0 - 85.0 = 5.50\times x[/tex]

[tex]132.0 = 5.50\times x[/tex]

Solve for x

[tex]x = \frac{132.0}{5.50}[/tex]

[tex]x = 24[/tex]

So, the total number of packages that can be bought for $322.00 is:

[tex]Total = 10 + 10 + 24[/tex]

[tex]Total = 44[/tex]

Hence, a total of 44 packages of paper can be bought for $322.00