Alan's wife sends him to the store to buy pickles and ice cream. Ice cream cost 5 dollars per pound and pickles costs 2 dollars per pound. Alan has 40 dollars in his wallet.

Let x be the number of pounds of ice cream and y be the number of pounds of pickles that Alan purchases. State the inequality that represents his budget, and graph the solution that represents the possible combinations of x and y. Express your answer with the standard form ax+by on the left side.

The number of pounds of ice cream multiplied by 5 dollars per pound plus the number of pounds of pickles multiplied by 2 dollars per pound must be equal at most to $40

so

The inequality that represent this situation is

[tex]5x+2y \leq 40[/tex]

using a graphing tool

The solution is the triangular shaded area

Remember that the number of pounds cannot be a negative number

see the attached figure

ap8997154 ap8997154 · Answer 2 · 2022-03-23T11:18:21+01:00

Inequalities help us to compare two unequal expressions. The inequality that can represent this situation is 5x+2y≤40.

What are inequalities?

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.

It is mostly denoted by the symbol <, >, ≤, and ≥.

As it is given that the cost of a pound of ice cream is $5, while x is the number of pounds of ice cream and the cost of pickles is $2, while y is the number of pounds of pickles that Alan purchases.

Therefore, the cost of ice cream that Alan bought is 5x and the total cost of pickle is 2y.

Now, the total cost of the ice cream should be equal to $40 or less than that because Alan has only $40 in his wallet.

Thus, the total cost of the ice cream and pickle can be written as,

[tex]5x+2y\leq 40[/tex]

The graph that represents this situation is in the image below.

Hence, the inequality that can represent this situation is 5x+2y≤40.

Learn more about Inequality:

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