## To write an equation for the cost (c) of Legal Eagles in terms of the length of the consultation time (t), we can use the given information that Legal Eagles charges a consultation fee of $100 plus $40 per hour. This can be expressed as:

CostLE = 100 + 40t

Similarly, for A-1 Attorneys, the cost (c) of the consultation in terms of time (t) can be written as:

CostA1 = 60t

Now, let's create a table of values showing the cost of each legal firm over a 6-hour period:

| Time (t) | Legal Eagles (CostLE) | A-1 Attorneys (CostA1) |

| -------- | -------------------- | --------------------- |

| 1 | 140 | 60 |

| 2 | 180 | 120 |

| 3 | 220 | 180 |

| 4 | 260 | 240 |

| 5 | 300 | 300 |

| 6 | 340 | 360 |

Next, let's graph the results:

(cost) ^

(USD) 400 | Legal Eagles (CostLE)

350 | /

300 | /

250 | /

200 | /

150 |--------------------- Intersection point

100 | /

50 | /

0 |--------------------- A-1 Attorneys (CostA1)

0 1 2 3 4 5 6 (time)

By looking at the graph, we can see that the lines representing the cost of Legal Eagles and A-1 Attorneys intersect at the point where the costs are the same. This point represents the number of hours of consultation time at which both legal firms cost the same.

To find this intersection point, we can equate the two cost equations:

100 + 40t = 60t

Simplifying this equation, we get:

100 = 20t

Dividing both sides by 20, we find:

t = 5

Therefore, at 5 hours of consultation time, both legal firms will cost the same.

To determine which firm gives more consultation time for $420, we can plug in the given cost value into the cost equations and solve for t:

CostLE = 420

420 = 100 + 40t

320 = 40t

t = 8

CostA1 = 420

420 = 60t

t = 7

By comparing the values of t, we can see that A-1 Attorneys give more consultation time (7 hours) for $420 compared to Legal Eagles (8 hours).

Based on the cost and consultation time, Mrs. Walsh should choose A-1 Attorneys as they provide more consultation time for $420.