Question

Laura needs to buy chips and soda for the guests at her party. Each large bag of chips cost $2.40 and each large bottle of soda cost $2.00. She has $48.00 to spend. Part A Create an inequality using two variables to represent this situation. Be sure to explain the meaning of each variable.Part B Which of the following graphs represent the number of chips and soda bottles that Laura can buy? Part C Which combination of bottles of soda and bags of chips can Laura buy?

Answer 1

Part A.

To write the inequality we have to introduce variables that represent the things Laura needs to buy. For this reason let x be the number of sodas she buys and let y be the number of chips she buys.

Now, we know that each bag of chips cost $2.40 then tha ammount she spends in chips will be

`2.4y`

Following the same reasoning, the ammount she spends in sodas will be

`2x`

The total ammount she spends will be the sum of each ammount, that is:

`2x+2.4y`

Finally, we know that Laura has $48, so she can only spend less or equal this ammount.

Therefore the inequality representing this situation is

`2x+2.4y\leq48`

Part B.

To graph this inequality, first we have to graph the line given by

`2x+2.4y=48`

Doing this we obtained the following graph

Now we need to decide which semi plane represent the solution set of the inequality. Since we have a less or equal sign the right choice is the left one, then the graph of the inequality is

Therefore the graphs representing the number of chips and soda bottles Laura can buy is option B.

Part C.

To determine which combination of bottles of soda and chips Laura can buy we can graph the options we have. Remember that the x-axis represents the soda and the y-axis the chips. Hence the option we have will be equivalent to the points (4,24), (12,8), (16,8) and (28,4). Graphing this points we have

The only option allowed is the one that lies within the shaded region, therefore Laura can buy 12 bottles of soda and 8 bags of chips.