Question

Erica bought 11 pizzas for $4.99) each and x two-liter bottles of soda for $1.99 each for her birthday party. She knows that she spent more than $80 before tax on the soda and pizza. What is the smallest possible value for x, the number of two-liter bottles that Erica purchased?​

Answer 1

x = 13 two-liter bottles

Explanation:

Since we're told that Erica spent more than $80, we'll need an inequality to solve.

We know that (cost of pizza * quantity of pizza) + (cost of soda * quantity of soda) > $80

If we allow p to represent the number of pizzas and b to represent the number of soda bottles, our equation is

4.99p + 1.99b > 80

Since we also know that she bough 11 pizzas, we can plug this in for p. Then, we'll simply have to solve for b:

`4.99(11)+1.99b > 80\\54.89+1.99b > 80\\1.99b > 25.11\\b > 12.618\\b > 13`

We had to round the 12.618 up to 13 for two reasons:

• We cannot have a fraction of a soda bottle, so only whole numbers make sense
• A value of 12.6 for b would make the cost less than 80, but Erica knows that her cost was more than 80

We can check our answer by plugging in 13 for b and seeing whether the value from 1.99 * 13 + 4.99 * 11 is greater than 80

4.99(11) + 1.99(13) > 80

54.89 + 25.87 > 80

80.76 > 80