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User Radzak
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System of Inequalities

Jocelyn is pregnant and she needs to consume at least 500 more calories per day.

She will do that by buying bananas and granola bars from a store.

Each banana costs $0.35 and each bar costs $2,50 each.

Let b=number of bananas and g= number of granola bars.

The total cost of bananas and granola bars is

0.35b + 2.50g

Jocelyn has a budget of $15. This means the total cost cannot exceed that amount of money:

0.35b + 2.50g ≤ 15

This is the first inequality to model the situation.

Now we consider the calories.

Each banana has 90 calories and each granola bar has 150 calories. The total calories are:

90b + 150g

This total must be at least 500 calories, thus:

90b + 150g ≥ 500

That is the second inequality.

Summarizing the system of inequalities is:

0.35b + 2.50g ≤ 15

90b + 150g ≥ 500

Let's test if Jocelyn can buy b=5 bananas and g=6 granola bars. Substituting those values in both inequalities:

0.35*5 + 2.50*6 ≤ 15

16.75 ≤ 15

90*5 + 150*6 ≥ 500

1350 ≥ 500

The first inequality is not true and the second one is true. Since both of them must be satisfied, the answer is NO, she cannot buy 5 bananas and 6 granola bars. In this case, she has not enough budget

User Tobiasfried
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