SOLUTION: A travel agency offers two Boston trips. Plan A includes hotel accommodations for three nights and two pairs of baseball tickets for $645. Plan B includes hotel accommodations for

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Question 1205627: A travel agency offers two Boston trips. Plan A includes hotel accommodations for three nights and two pairs of baseball tickets for $645. Plan B includes hotel accommodations for five nights and four pairs of baseball tickets for $1135. a. Let x represent the cost of one night’s hotel stay and y represent the cost of one pair of baseball tickets. Write a system of equations you could use to solve this problem for the cost of the hotel and baseball tickets.
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
x = number of nights at a hotel.
y = number of pairs of baseball tickets.

option A has 3 nights and 2 pairs of tickets.
option B has 5 nights and 4 pairs of tickets.

two equations that need to be solved simultaneously are:

3x + 2y = 645 for option A.
5x + 4y = 1135 for option B.

multiply both sides of the first equation by 2 and leave the second equation as is to get:

6x + 4y = 1290
5x + 4y = 1135

subtract the second equation from the first to get:

x = 155

solve for y in the first equation to get:

6*155 + 4y = 1290
4y = 1290 - 930 = 360
y = 360/4 = 90

you have x = 155 and y = 90
that's 155 a night at a hotel and 90 for a pair of tickets.
that's your solution.

you can confirm by replacing x with 155 and y with 90 in your two original equations.

you will get 3*155 + 2 * 90 = 645 and you will get 5*155 + 4*90 = 1135, as i did.