Question

Adam is ordering pizza for a company party that he needs to have catered. Company A charges $8 for each pizza and a delivery/set-up fee of $45. Company B charges $12 for each pizza and a delivery/set-up fee of $5. Which inequality can be used to find x, the least number of pizzas that can be ordered so that the total charge for Company A is less than the total charge for Company B?

Answer 1

Inequality is
`8x+45 < 12x+5` and value of x>10.

Explanation:

Given : Adam is ordering pizza for a company party that he needs to have catered.

Company A charges $8 for each pizza and a delivery/set-up fee of $45. Company B charges $12 for each pizza and a delivery/set-up fee of $5.

To find : Which inequality can be used to find x, the least number of pizzas that can be ordered so that the total charge for Company A is less than the total charge for Company B?

Solution : Let x be the number of pizza

Company A charges $8 for each pizza and a delivery/set-up fee of $45.

Total charge of Company A is
`8x+45`

Company B charges $12 for each pizza and a delivery/set-up fee of $5.

Total charge of Company B is
`12x+5`

The total charge for Company A is less than the total charge for Company B

i.e, Inequality form
`8x+45 < 12x+5`

`\Rightarrow 45-5< 12x-8x`

`\Rightarrow 40< 4x`

`\Rightarrow (40)/(4)< x`

`\Rightarrow 10< x`

or x> 10

Therefore, Inequality is
`8x+45 < 12x+5` and value of x>10.