Help on algebra homework please. I would love to see how you did it, but just the basic is fine.
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Help on algebra homework please. I would love to see how you did it, but just the basic is fine.

[From: ] [author: ] [Date: 11-08-31] [Hit: ]
What is the minimum number of days that Shirleys vacation should be for M & N Travel to have a better deal?Equate these two.x = 9.16666.........
Write and solve an equation for each situation.

Problem: Tracey is looking at two different travel agencies to plan her vacation. ABC Travel offers a plane ticket for $295 and a rental car for $39 a day. M & N Travel offers a plane ticket for $350 and a rental car for $33 per day. What is the minimum number of days that Shirley's vacation should be for M & N Travel to have a better deal?

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ABC Travel's offer:

$295 + $39x

M & N Travel's offer:

$350 + $33x

Equate these two.

$295 + $39x = $350 + $33x

$6x = $55

Divide both sides by $6

x = 9.16666...

The minimum number of days would be 10 days.

Hope this helps.

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Well, first of all, seems that Tracey changed her name to Shirley. Never mind, let's try to solve the problem here:

Call x the number of days Tracey-Shirley takes for her vacation.

The total cost C1 traveling by ABC plan is:

C1 = 295 + 39x

The total cost C2 traveling by M&N plan is:

C2 = 350 + 33x

If traveling M&N is meant to be a better deal, it means that:

C2 < C1

or:

350 +33x < 295 + 39x

gathering all x's terms at the right side and all pure numerical terms at the left side of the inequation we have:

350 - 295 < 39x - 33x

55 < 3x

55/3 < x

11 < x

or:

x > 11

Answer: more than 11 days in vacation makes M&N plan a better deal
Have a nice trip Tracey-Shirley!

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Let d = number of days, A = ABC travel's cost, M = M & N Travel's cost. Then:

A = 295 + 39d
M = 350 + 33d

We want to find d such that A = m, so

295 + 39d = 350 + 33d
39d = 350 + 33d - 295 subtract 295 from each side
39d - 33d = 350 - 295 subtract 33d from each side
6d = 55 calculate each side
d = 55 / 6
d = 9 1/6 days

If Shirley stays more than 9 days, M & N Travel will cost less.

-
let x be the minimum number of days

expenditure for ABC plan
295 + 39 x

expenditure for M&N plan

350 + 33x

=> 350 + 33x < 295 + 39x

=> 55 < 6x

=> 6x > 55

x > 55/6 => x > 9 1/6

minimum number of days for better deal through M&N = 10 days

-
ABC - 295 + 39x > MN 350 +33x

-295 - 33x -295 - 33x
______________________________________…
0 + 6 x > 55 0x

(6x > 55) divide by 6 x > 55/6

9.17 days
1
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