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Brock bought 4 candy bars and 2 packs of gum at the gas station and spent $9.80. Iwo packs of gum cost the same as three candy bars. Let g represent the cost of a pack of gum and c represent the cost of a candy bar.

a.
Write a system of equations to represent this situation.
11461
29-
4.50
9,80
= 4.40
2.45 S
1
b.
Solve the system and write a sentence explaining your results.

User Frezik
by
7.8k points

1 Answer

4 votes

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.

User Vlad Stefanescu
by
8.2k points