Question

Q#1: Amanda and Lisa are playing games at the arcade. Amanda started with $15, and the machine she is playing costs $0.75 per game. Lisa started with $13, and her machine costs $0.50 per game. After how many games will the two girls have the same amount of money remaining?
Q#2:The Lone Star Shipping Company charges $14 plus $2 a pound to ship an overnight package. Discount Shipping Company charges $20 plus $1.50 a pound to ship an overnight package. For what weight is the charge the same for the two companies?

Answer 1

Answer: For question one its 8

Step-by-step explanation: Let A be the variable for Amanda! The amount of money she has for x amount of time. We know that lisa has $13 and she is spending .50 every game. The equation for this would be L=13-0.5x. SO to solve this problem of when they both will have the same amount of money use the equation. 15- 0.75x=13 - 0.5x then you will switch the equation around. So the next step would look like 15-13= -0.5x + 0.75x! Then you'll get 2=0.25x change that to a fraction and you'll get 1/4 and 8=x!

Im so sorry if this is confusing!

Answer 2

Let D = the amount of money Deanna has after x games.

We know Deanna started with $15 and she spends 0.75 per game, so we can make the following equation:
D = 15 - 0.75x

Let L = the amount of money Lisa has after x games.

We know Lisa started with $13 and she spends 0.50 per game, so we can make the following equation:
L = 13 - 0.5x

The question is asking how many games need to be played for L and D to be equal, so just equate L and D and solve for x:

D = L
15 - 0.75x = 13 - 0.5x
15 - 13 = -0.5x + 0.75x
2 = 0.25x
2 = (1/4)x
8 = x

Therefore they need to play 8 games each to have the same amount of money.