Question

Delicious Doing caterers events at a flat rate $500 plus $100 per hour after the first 2 hours. Cathy's Catering has a flat rate of $620 per event plus $70 per hour after the first three hours. What is the most amount of hours you could hire Cathy's Catering for and it cost less than Delicious Doings? Write an inequality that could be used to solve this problem

Answer 1

3 hours

Explanation:

Let the number of hours worked = x

Delicious Doing caterers events at a flat rate $500 plus $100 per hour after the first 2 hours.

$500 + $100 × x

500 + 100 × 1

After the first 2 hours = $500 + $100

= $600

After the first 3 hours = $500 + $100 × 2

= $700

Cathy's Catering has a flat rate of $620 per event plus $70 per hour after the first three hours.

$620 + $70 × x

620 + 70x

After the first 3 hours

= $600 + $70

= $670

What is the most amount of hours you could hire Cathy's Catering for and it cost less than Delicious Doings?

The Inequality is given as:

Cathy's Catering for < Delicious Doings

620 + 70x < 500 + 100x

Collect like terms

620 - 500 < 100x - 70x

120 < 30x

120/30 < x

4 < x

Therefore, the most amount of hours the most amount of hours you could hire Cathy's Catering for and it cost less than Delicious Doings is 3 hours