Question

Samantha is going on vacation for the summer and is trying to choose between two different plans. The first plan costs $450 for 3 days at a hotel and 2 days at an amusement park. The second plan offers 5 days at the same hotel and 3 days at the amusement park for $700. The cost of 1 day at the hotel and the amusement park is the same under both plans. How much does a 1 day trip to the amusement park cost?
Question 9 options:
1) $50
2) $75
3) $150
4) $200

Answer 1

x = cost of 1 day in hotel
y = cost of 1 day at the amusement park

the equation for plan A is: 3x + 2y = 450
the equation for plan B is: 5x + 3y = 700

then solving for x:

-3 * (3x + 2y = 450) = -9x - 6y = -1350
2 * (5x + 3y = 700) = 10x + 6y = 1400

the y's cancel out leaving you with x = 50

so option 1 is the answer

let me know if you need me to explain how to solve the two equations with more depth

Answer 2

Can you help with this?
What is a possible first step to eliminate a variable in the following system?
7x - 9y = 2
3x - 6y = -4
Question 3 options:
1) Multiply the first equation by 2 and the second equation by -3.
2) Multiply the first equation by -3 and the second equation by -2.
3) Multiply the first equation by 7 and the second equation by 3.
4) Multiply the first equation by -2 and the second equation by 4.

Answer 3

The best way to solve this question is to just try out each answer. When you work out 2 3 and 4, nothing significant happens.

but when you work out number 1:

2 * (7x - 9y = 2) = 14x - 18y = 4
-3 *(3x - 6y = -4) = -9x +18y = 12

what the problem wants you to notice is that the "-18y" and "18y" cancel out, so the answer is 1

I can help you solve the equation through for x and y if you need to do that as well