Question

Maya and Nikki are buying school supplies. Maya pays $28.75 for 4 notebooks and 3 packs of pens. Nikki pays $25.75 for 2 notebooks and 5 packs of pens. When n is the price, in dollars, of a notebook and p is the price, in dollars, of a package of pens, this situation is modeled by the given system of equations. Solve for n and p.

a) n = 5, p = 4

b) n = 4, p = 5

c) n = 6, p = 3

d) n = 3, p = 6

Answer 1

Maya and Nikki can buy notebooks at a price of $5 each and packs of pens at a price of $3.25 each.

Step-by-step explanation:

To solve this problem, we can start by setting up a system of equations using the given information. Let's assign 'n' as the price of a notebook and 'p' as the price of a pack of pens.

From the first sentence, we can write the equation: 4n + 3p = 28.75. And from the second sentence, we can write the equation: 2n + 5p = 25.75.

Next, we can solve this system of equations using either substitution or elimination. By eliminating 'n', we can multiply the first equation by 2 and the second equation by 4, resulting in: 8n + 6p = 57.50 and 8n + 20p = 103.00. Subtracting the first equation from the second, we get: 14p = 45.50. Dividing both sides by 14, we find that p = 3.25.

Finally, we can substitute the value of 'p' back into one of the original equations to find 'n'. Using the first equation, we have: 4n + 3(3.25) = 28.75. Solving for 'n', we get n = 5.

Therefore, the solution to the system of equations is n = 5 and p = 3.25.