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The soccer team is planning to sell health bars for a fundraiser. The prices of purchasing health bars from two different companies are represented by the system of equations shown, where [tex]\(x\)[/tex] is the number of bars purchased and [tex]\(y\)[/tex] is the total cost in dollars.

Company A: [tex]\(y = 0.75x\)[/tex]
Company B: [tex]\(y = 10 + 0.50x\)[/tex]

How many bars would the team need to purchase from each company in order for the total cost to be equal?

A. 6
B. 8
C. 30
D. 40



Answer :

GinnyAnswer
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

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