Question

An employee at the College Bookstore was restocking the shelves before the start of a new term. Michelle is trying to figure out how many items were bought. The notebooks were bought for $5 each and the packs of pens were $3 each. If there are 97 items, and the total spent on the supplies was $381, find out how many of each item (notebooks and pen packs) were purchased.a. write to equations created from the scenario.b. solve using Elimination Method. Show all the steps for the Elimination Method to earn pointsc. Solve using Substitution Method. Show all steps for the Substitution Method to earn points.

Answer 1

notebooks = $5 each

Pack of pens = $3 each

number of notebooks = n

number of pack of pens = p

total items = 97

n + p = 97

total spent on supplies $381

5n + 3p = 381

a)

n + p = 97

5n + 3p = 381

b)

Multiply the first equation by 5

5n + 5p = 485

Then subtract the second equation to eliminate n

5n+5p=485

-

5n+3p=381

__________

0n +2p= 104

p= 104/2

p= 52

Replace p on any equation and solve for n

n+p=97

n + 52 = 97

n= 97-52

n= 45

n=45, p=52

c.

Solve the first equation for n

n+p=97

n= 97-p

Replace n=97-p on the second equation

5n + 3p = 381

5 (97-p) + 3p = 381

Solve for p

485 - 5p + 3p = 381

-2p = 381 - 485

-2p= -104

p= -104/-2

p= 52

Replace p=52 on the first equation and solve for n

n + p= 97

n + 52 = 97

n= 97-52

n= 45

n=45,p=52