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?
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?
-
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.
$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.
-
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!
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!
-
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.
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
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
-295 - 33x -295 - 33x
______________________________________…
0 + 6 x > 55 0x
(6x > 55) divide by 6 x > 55/6
9.17 days