Question

Angela is playing a video game. In this game, players can score points only by collecting coins and stars. Each coin is worth c points, each star is worth s points. The first time she played, Angela scored 700 points. She collected 20 coins and 10 stars. The second time she played, Angela scored 850 points. She collected 25 coins and 12 stars. Which system of equations can be used to correctly determine the values of c and s?\

Answer 1

To determine the values of c and s, we can set up a system of equations using the given information. We can solve this system of equations using the method of substitution.

Step-by-step explanation:

To determine the values of c and s, we can set up a system of equations using the given information:

Equation 1: 20c + 10s = 700

Equation 2: 25c + 12s = 850

We can solve this system of equations using the method of elimination or substitution. Let's use the method of substitution:

From Equation 1, we can solve for c:
c = (700 - 10s) / 20

Substitute this expression for c into Equation 2:

(700 - 10s) / 20 * 25 + 12s = 850

Simplify and solve for s:

1750 - 250s + 240s = 850
-10s = -900
s = 90

Now substitute the value of s back into Equation 1 to solve for c:

20c + 10(90) = 700
20c + 900 = 700
20c = -200
c = -10

Therefore, the values of c and s are -10 and 90, respectively.