Question

select the correct answer.
a daycare purchases two type of snacks, granola bars and fruit rolls. one week, they purchase 10 packs of granola bars and 6 packs of fruit rolls for a total of 162 snacks. the next week, they purchase 7 packs of granola bars and 12 packs of fruit rolls for a total of 200 snacks.
how many snacks are in one pack of granola bars and one pack of fruit rolls?

a. there are 6 snacks in one pack of granola bars and 14 snacks in one pack of fruit rolls.

b. there are 8 snacks in one pack of granola bars and 12 snacks in one pack of fruit rolls.

c. there are 14 snacks in one pack of granola bars and 6 snacks in one pack of fruit rolls.

d. there are 12 snacks in one pack of granola bars and 8 snacks in one pack of fruit rolls.

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Explanation:

Step1: Define variables

Let \( x \) be the number of snacks in one pack of granola bars and \( y \) be the number of snacks in one pack of fruit rolls.

Step2: Set up equations

From the first week: \( 10x + 6y = 152 \)
From the second week: \( 7x + 12y = 200 \)

Step3: Solve the system of equations

Multiply the first equation by 2: \( 20x + 12y = 304 \)
Subtract the second equation from this new equation:
\( (20x + 12y) - (7x + 12y) = 304 - 200 \)
\( 13x = 104 \)
\( x = 8 \)
Substitute \( x = 8 \) into the first equation: \( 10(8) + 6y = 152 \)
\( 80 + 6y = 152 \)
\( 6y = 72 \)
\( y = 12 \)

Answer:

B. There are 8 snacks in one pack of granola bars and 12 snacks in one pack of fruit rolls.