Question

You buy 6 health bars and 2 health drinks for $20. Your friend buys 5 health bars and 3 health drinks for $22. What is the cost of each health bar? and of each health drink?(2 points)
Each health bar costs $
and each health drink costs $
.

Answer 1

Let's denote the cost of each health bar as \( b \) and the cost of each health drink as \( d \).

From the information provided, we can set up the following two equations based on the purchases:

1. For your purchase:
\[
6b + 2d = 20
\]

2. For your friend's purchase:
\[
5b + 3d = 22
\]

Now we can solve these equations step by step.

First, let's simplify the first equation:
\[
6b + 2d = 20
\]
Dividing the entire equation by 2:
\[
3b + d = 10 \quad \text{(Equation 1)}
\]

Now, we will rearrange this to find \( d \):
\[
d = 10 - 3b \quad \text{(Equation 2)}
\]

Next, we substitute Equation 2 into the second equation (for your friend's purchase):
\[
5b + 3(10 - 3b) = 22
\]

Expanding this:
\[
5b + 30 - 9b = 22
\]

Combining like terms:
\[
-4b + 30 = 22
\]

Subtracting 30 from both sides:
\[
-4b = 22 - 30
\]
\[
-4b = -8
\]

Dividing by -4:
\[
b = 2
\]

Now that we have the cost of each health bar, we can find the cost of each health drink using Equation 2:
\[
d = 10 - 3b
\]
Substituting \( b = 2 \):
\[
d = 10 - 3(2) = 10 - 6 = 4
\]

Thus, the costs are:
- Each health bar costs \( \$2 \)
- Each health drink costs \( \$4 \)

Final answer:
Each health bar costs $2 and each health drink costs $4.