To determine how many bars the soccer team needs to purchase for the total cost from both companies to be equal, let's solve the given system of linear equations step-by-step.
We have two companies with the following cost equations:
- Company A: [tex]\( y_A = 0.75x \)[/tex]
- Company B: [tex]\( y_B = 10 + 0.50x \)[/tex]
We need to find the value of [tex]\( x \)[/tex] (the number of health bars) for which the total cost from both companies is the same. Therefore, we set the equations equal to each other:
[tex]\[
0.75x = 10 + 0.50x
\][/tex]
To isolate [tex]\( x \)[/tex], we first subtract [tex]\( 0.50x \)[/tex] from both sides of the equation:
[tex]\[
0.75x - 0.50x = 10
\][/tex]
This simplifies to:
[tex]\[
0.25x = 10
\][/tex]
Next, we solve for [tex]\( x \)[/tex] by dividing both sides by 0.25:
[tex]\[
x = \frac{10}{0.25}
\][/tex]
Calculating the right-hand side:
[tex]\[
x = 40
\][/tex]
So, the soccer team needs to purchase 40 health bars for the total cost from both companies to be equal. Therefore, the correct answer is:
40
