Mildred makes $3 an hour babysitting and $6 an hour when she works at Wendys. Her parents do not want her working more than 20 hours per week. Mildred would like to earn at least $70 a week. Write a system of inequalities that show the number of hours she could work at each job. Graph the system. Write at least four possible solutions. THANK YOU

hrs at Wendy's ---- x

hrs babysitting --- 20-x

6x + 3(20-x) ≥ 70

solve for x, the rest is easy

To write a system of inequalities representing Mildred's work hours at each job, we can use the following information:

1. Mildred makes $3 per hour babysitting, so the amount she earns from babysitting in a week (B) can be represented as: B = 3h, where h represents the number of hours she babysits.

2. Mildred makes $6 per hour at Wendy's, so the amount she earns from working at Wendy's in a week (W) can be represented as: W = 6t, where t represents the number of hours she works at Wendy's.

3. Mildred's parents do not want her working more than 20 hours per week, so the total number of hours she works (h + t) must be less than or equal to 20: h + t ≤ 20.

4. Mildred wants to earn at least $70 per week, so the sum of her earnings from both jobs (B + W) must be greater than or equal to 70: B + W ≥ 70.

Graphing the system of inequalities:

To graph the system, we can create a coordinate plane and plot the feasible region that satisfies the given constraints.

First, let's rewrite the inequalities in slope-intercept form:
B = 3h --> h = (1/3)B
W = 6t --> t = (1/6)W
h + t ≤ 20
B + W ≥ 70

Now, let's select some values and substitute them to find corresponding points on the graph:

Possible solution 1:
Let's assume Mildred babysits for 5 hours (h = 5):
So, B = 3h = 3(5) = 15
Substituting these values, we get: 5 + t ≤ 20 and 15 + W ≥ 70
Simplifying, we have: t ≤ 15 and W ≥ 55

Possible solution 2:
Let's assume Mildred works at Wendy's for 7 hours (t = 7):
So, W = 6t = 6(7) = 42
Substituting these values, we get: h + 7 ≤ 20 and B + 42 ≥ 70
Simplifying, we have: h ≤ 13 and B ≥ 28

Possible solution 3:
Let's assume Mildred babysits for 3 hours (h = 3):
So, B = 3h = 3(3) = 9
Substituting these values, we get: 3 + t ≤ 20 and 9 + W ≥ 70
Simplifying, we have: t ≤ 17 and W ≥ 61

Possible solution 4:
Let's assume Mildred works at Wendy's for 8 hours (t = 8):
So, W = 6t = 6(8) = 48
Substituting these values, we get: h + 8 ≤ 20 and B + 48 ≥ 70
Simplifying, we have: h ≤ 13 and B ≥ 22

Now, plot each feasible region on the graph and shade the region that satisfies all the conditions. The intersection of all shaded regions represents the feasible region.