Question

Jocelyn is pregnant and needs to eat at least 360 more calories a day than usual. When buying groceries one day with a budget of $11.25 for extra food, she buys bananas that have 50 calories each and granola bars that have 90 calories each. The bananas cost $0.75 each and the granola bars cost $2.25 each.Write a system of 2 inequalities to model this situation. Use "x" for the number of bananas and "y" for the number of granola bars.

Answer 1

`\begin{gathered} 50x\text{ + 90y}\ge\text{ 360} \\ 0.75x\text{ + 2.25y}\leq11.25 \end{gathered}`

Step-by-step explanation:

Here, we want to write a system of inequalities

From the given question:

She needs at least 360 calories

The bananas have 50 calories each and we have x number to be bought

That is a total of 50 * x = 50x calories from bananas

The granola bars have 90 calories each, so for y number of granola, we have a total of y * 90 = 90y calories

She needs at least 360 calories more

Mathematically, that means:

`50x\text{ + 90y }\ge360`

Now, the bananas cost $0.75 each and the granola cost $2.25 each

for x bananas, we have 0.75 * x = $0.75x cost

For the granola, we have a cost of $2.25 each for them and that is a total of 2.25 * y = $2.25y

The budget values cannot be exceeded, so we have:

`0.75x\text{ + 2.25y }\leq\text{ 11.25}`

Thus, the system of inequalities would be:

`\begin{gathered} 50x\text{ + 90y}\ge360 \\ 0.75x\text{ + 2.25y}\leq11.25 \end{gathered}`