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