Answer: The cost of a pack of gum (g) is approximately $2.10.
The cost of a candy bar (c) is approximately $1.40.
Step-by-step explanation: To solve this problem, we need to set up a system of equations using the given information.
Let's first assign variables to represent the cost of a pack of gum (g) and the cost of a candy bar (c).
From the problem, we know that Brock bought 4 candy bars and 2 packs of gum and spent $9.80. This can be expressed as:
4c + 2g = 9.80 (Equation 1)
We are also given that two packs of gum cost the same as three candy bars. Mathematically, this can be represented as:
2g = 3c (Equation 2)
Now we have a system of two equations with two variables. We can solve this system to find the values of g and c.
Let's substitute the value of 3c from Equation 2 into Equation 1:
4c + 2g = 9.80
4(2g/3) + 2g = 9.80
(8g/3) + 2g = 9.80
Multiply both sides of the equation by 3 to eliminate the fraction:
8g + 6g = 29.40
14g = 29.40
Divide both sides by 14:
g = 29.40/14
g ≈ 2.10
Now, substitute the value of g into Equation 2 to find the value of c:
2(2.10) = 3c
4.20 = 3c
Divide both sides by 3:
c = 4.20/3
c ≈ 1.40
So, the cost of a pack of gum (g) is approximately $2.10 and the cost of a candy bar (c) is approximately $1.40.
To summarize:
- The cost of a pack of gum (g) is approximately $2.10.
- The cost of a candy bar (c) is approximately $1.40.