Question

1. Sherry started with $18 in her cash box for the concession stand

and is selling bags of chips for 50 cents each. Damien started with
$12 in his concession stand cash box and is selling ice cream
sandwiches for 75 cents each. The total amount of money in their
cash box depends on the number of items, x, sold. Write an equation
or inequality that represents the situation when Sherry and Damien
will have the same amount of money in their cash boxes.

Answer 1

The equation that represents the situation when Sherry and Damien will have the same amount of money in their cash boxes is 18 + 0.5x = 12 + 0.75x

Solution:

Given that

Initial amount of sherry in cash box = $18

Sherry is selling bags of chips.

Price of 1 bag of chips = 50 cents = $ 0.5

Initial amount of Damien in cash box = $12

Damien is selling ice cream sandwich .

Price of 1 ice cream sandwich = 75 cents = $ 0.75

Lets create expression of amount in cash box for sherry and daimen when "x" items are sold.

In case of Sherry price of "x" bags of chips
`=\text { price of } 1 \text { bag of chips } *`

Amount in Sherry cash box after "x" items are sold = initial amount + price of "x" bags of chips

Amount in Sherry cash box after "x" items are sold = 18 + 0.5x ------ (1)

In case of Damien price of "x" ice cream sandwich =
`=\text { price of } 1 \text { ice cream sandwich } * x=0.5 x`

Amount in Damien cash box after "x" items are sold = initial amount + price of "x" ice cream sandwich

Amount in Damien cash box after "x" items are sold = 12 + 0.75x ------ (2)

As we required expression when amount in both the cash boxes must be equal, on equating (1) and (2) we get

18 + 0.5x = 12 + 0.75x

Hence expression 18 + 0.5x = 12 + 0.75x represents a condition when amount in both the cash boxes will be same.