PLEASE HELP ASAP, I HAVE 10 MINUTES ;
Arianna and her children went into a grocery store where they sell peaches for $1 each and mangos for $0.50 each. Arianna has $9 to spend and must buy at least 13 peaches and mangos altogether. If x represents the number of peaches purchased and y represents the number of mangos purchased, write and solve a system of inequalities graphically and determine one possible solution.

Answer:

Step-by-step explanation:

when 13 bought we find these inequalities

x + 12y < 7  no

2x + 11y < 7.5 no

3x + 10y < 8 no

4x + 9y < 8.5 no

5x + 8y >  9  yes

When 14 bought we find these inequalities

x + 13y < 7.5 no

2x + 12y < 8 no

3x + 11y < 8.5 no

4x + 10y > 9 yes  

We want to find and solve a system of inequalities to determine some possible solutions to Arianna's situation.

The possible solution is:

x = 2

y = 12

And the graph can be seen at the end.

Now let's see how to solve this.

First, we need to write the system of inequalities, the information given is:

Now we can define the variables:

Then we must have:

x + y ≥ 13   (this means that she buys at least 13 fruits)

x*$1 + y*$0.50 ≤ $9  (this means that she can't spend more than $9)

Now we just need to graph these two lines, we can rewrite them as:

y ≥ 13 - x

y ≤ $9.00/$0.50 - x*$1/$0.50 = 18 - x*2

Then we just need to graph the two lines, and shade the region above the first one, and the region below the second one, the graph can be seen below:

Any point inside the double shaded region in the first quadrant is a possible solution. (we restrict only to the first quadrant because we can not use negative values for x nor for y).

Then a possible solution that we could choose is:

x = 2

y = 12

This means that she buys 2 peaches and 12 mangos.

If you want to learn more, you can read:

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